While much attention has been given to the use of principles in biomedical ethics and increasing attention is given to alternative theoretical approaches, relatively little attention has been devoted to the critical task of how one resolves conflicts among competing principles. After summarizing the system of principles and some problems in conceptualizing the principles, several strategies for reconciling conflicts among principles are examined including the use of single-principle theories (pure libertarianism, pure utilitarianism, and pure Hippocratism), balancing theories, conflicting appeals (...) theories, and lexical ordering. Then a mixed strategy is proposed in which consequentialist principles are balanced between themselves as are nonconsequentialist principles, after which the result of balancing the nonconsequentialist principles is lexically ranked over the result of balancing the consequentialist ones. Finally, strategies involving specifying and rule generation are discussed concluding that most current specification and rule-generating theories must involve some degree of lexical ordering of principles. (shrink)

Within universities, a tension exists between research and teaching and learning, where research is often accorded a higher status creating a Cinderella effect by rendering teaching and learning of lesser importance. World university rankings, also referred to as global rankings, are contentious although they have become a permanent feature of the higher education system internationally. Lindsay argues that institutions have emphasized the importance of publications and prestige, which contribute to national and institutional reputation. Publications increase rankings thereby contributing to the (...) lower prestige given to excellent teachers as compared to excellent researchers. This has consequently led to a decline in the attention given to teaching. Pressure exists in the HE system to play the ranking game without acknowledging that there are expertise and pockets of teaching excellence in universities. Through their performance criteria, global rankings are transforming universities into becoming similar and conforming to a single hierarchy. In order to compete in the global HE market and improve their rankings, some universities have adopted a business model to mitigate the effects of globalisation and have begun to view themselves and higher education as a business. Global ranking systems thus have the agency either to perpetuate teaching and learning as the Cinderella function in HE, through the ranking game or to holistically focus their performance criteria on all the core functions of universities. Ethical policy decision-making in higher is thus essential. (shrink)

Data-driven algorithms are currently deployed in several fields, leading to a rapid increase in the importance algorithms have in decision-making processes. Over the last years, several instances of discrimination by algorithms were observed. A new branch of research emerged to examine the concept of “algorithmic fairness.” No consensus currently exists on a single operationalization of fairness, although causal-based definitions are arguably more aligned with the human conception of fairness. The aim of this article is to investigate the degree of (...) this alignment in a case study inspired by a recent ruling of an Italian court on the reputational-ranking algorithm used by a food delivery platform. I relied on the documentation of the legal dispute to discuss the applicability, intuitiveness and appropriateness of causal models in evaluating fairness, with a specific focus on a causal-based fairness definition called “counterfactual fairness.” I first describe the details of the dispute and the arguments presented to the court, as well as the court’s final decision, to establish the context of the case study. Then, I translate the dispute into a formal simplified problem using a causal diagram, which represents the main aspects of the data generation process in the case study. I identify the criteria used by the court in ruling that the algorithm was unfair and compare them with the counterfactual fairness definition. The definition of counterfactual fairness was found to be well aligned with the human conception of fairness in this case study, using the court order rationale as a gold standard. (shrink)

The present contribution argues that transitive reasoning, as exemplified in paradigms of linear order construction in mental space, is associated with spatial effects. Starting from robust findings from the early 70s, research so far has widely discussed the symbolic distance effect. This effect shows that after studying pairs of relations, e.g., “A > B,” “B > C,” and “D > E,” participants are more correct, and faster in correct responding, the wider the “distance” between two elements within the chain (...) A > B > C > D > E. The SDE has often been given spatial interpretations, but alternatively, non-spatial models of the effect are also viable on the empirical basis so far, which means the question about spatial contributions to the construction of analog representations of rank orders is still open. We suggest here that laterality effects can add the necessary additional information to support the idea of spatial processes. We introduce anchoring effects in terms of showing response advantages for congruent versus incongruent pairings of presentation location on a screen on the one hand, and the hypothetical spatial arrangement of the order in mental space, on the other hand. We report pertinent findings and discuss anchoring paradigms with respect to their internal validity as well as their being rooted in basic mechanisms of trained reading/writing direction. (shrink)

I argue that we can generate intransitive preference orderings for a single person on the model of Sen's Libertarian Paradox.

There are some radical practices of asceticism, such as wearing ṣūf (wool clothes), traveling without provisions, choosing to be single, and avoiding earning a living by working, which were generally seen in the 2nd century A.H. and were subject to criticism with the formation of classical Ṣūfism. Criticisms of these practices have started to appear in the literature since the 3rd century A.H. Early Ṣūfī writers such as Al-Ḥakīm al-Tirmidhī, Muḥāsibī, Abū Saʿīd al-Kharrāz, al-Sarrāj focused on this issue and (...) criticized these practices. How are these practices of ascetics viewed in the sects that were formed and spread in the 6th and 7th centuries? Our research seeks the answer to this question, but limits it to the example of Abū l-Ḥasan al-Shādhilī, the founder of Shādhiliyya. This question is important in two respects: First of all, it is investigated whether the determination of some researchers that al-Shādhilī taught comfort in the face of worldly blessings is also correct. Because, among contemporary researchers, there are those who believe that al-Shādhilī wears ostentatious clothes, rides horses, encourages economic competitiveness, and is therefore open to benefiting from worldly blessings to the fullest. Secondly, it includes an investigation of the validity of the belief that these practices belong to an early period in the history of Sûfism and have been completely abandoned over time. Although al-Shādhilī seems to have completed his spiritual education in Morocco with his sheikh, he later went to Tunisia with the latent command of his master. We see that in his first years in Tunisia, he went into seclusion in a cave and was completely isolated from the society and engaged in worship in a way that reminds us of the practices of the early ascetics. But in the second phase of his life in Tunisia, he went to the city on a spiritual sign, socialized, started to give sermons to people, and started to behave more flexible about eating and drinking. al-Shādhilī specifically states that he did not prefer socialization at this stage, but with a spiritual sign. Later, he went to Egypt again with a spiritual sign and got married there, started to deal with agriculture, and continued to socialize by establishing relations with the rulers. Therefore, it can be said that this new social period is a break both from the radical practices of the early ascetics and from the early period in Tunisia itself. It is also seen that in this new period of al-Shādhilī, he did not wear the clothes of ascetics like sūf (wool clothes) and did not want his followers to wear them. He also encouraged to have a profession and was generally against traveling without provisions. But there are two points to be noted here: First, these milder and more comfortable practices should not lead to a search for comfort and luxury. He continued to keep his distance from worldly blessings and to advise asceticism. Secondly, he had some of his distinguished disciples make some practices of the ascetics. The reason for the existence of these seemingly contradictory practices is that while he recommends moderate and sustainable practices to the general public and his followers, he can make the specialized sūfis more strict and difficult practices. While he was encouraging work and earning in general, not ignoring experience, including avoiding work; not ignoring seclusion while leading to sociality in general; while generally suggesting to resort to occasions, he also follows a path of implementing and enforcing radical practices such as traveling without food. Thus, al-Shādhilī is able to encompass all the seemingly incompatible practices of the previous sūfi accumulation with a point of view of spiritual rank and hierarchy. (shrink)

Political scientists generally consider that the incentive for legislators to switch parties lies in their desire to be re-elected. While some scholars attribute defection to the legislators’ popularity and strong connections with their constituents which enable them to be re-elected without relying on party labels, others assert that legislators switch if they perceive that staying put might threaten their chances of re-election. In this paper, we find that the two assumptions, to some extent, contradict each other. More surprisingly, the two (...) contradictory hypotheses cohabit under the single non-transferable vote system. From an analysis of the switching in the Taiwanese Legislative Yuan, the empirical evidence shows that because of fierce intraparty competition in the multimember districts, not only barely elected but also top-ranked legislators switched party affiliation in order to avoid the loss in votes or even seats to their copartisans and to maximize their chances of re-election. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:The Establishment Hypothesis:Toward a More Integrated Theology of Holy OrdersDominic CerratoPreliminary ConsiderationsUnderstanding the ProblemThough the Sacrament of Holy Orders is a single sacrament consisting of three degrees, throughout its theological development, much of the focus has been on that of the priesthood. By priesthood I mean the two degrees that are sacerdotal in nature, the episcopate and the presbyterate. Given the growing understanding of the Eucharist in the (...) Tradition, and its intrinsic connection to the priesthood as its exclusive agent, this sacerdotal emphasis was a natural and organic development.1 Nonetheless, while revealing much, this sacerdocentrism, along with the adoption of the cursus honorum,2 had the unintended effect of obscuring the third level of the hierarchy, the diaconate.3 While the diaconate as an ancient order (Acts 6:1–6) would eventually be numbered among the major orders, being ordained non ad sacerdotium sed ad ministerium episcopi4 meant that deacons were not, in the same sense, related to the Eucharist as were priests. Consequently, much of [End Page 1275] what passed for diaconal theology is its liturgical role and charitable work among the poor. As observed by the Benedictine theologian Dom Augustinus Kerkvoorde just prior to the restoration of the diaconate, "there is, as far as we know, no independent theology of the diaconate. The number of authors and works should not delude us. None of them deals with the diaconate exclusively, say, to help deacons correctly understand and exercise their function in the Church."5 He goes on to characterize diaconal theology as fragments strewn throughout the various writings on orders in general, the priesthood, and the sacraments.6As later noted by the 2002 International Theological Commission on the Diaconate, this lack can be clearly observed in both the conciliar and post-conciliar documents on the diaconate. Of these, the commission wrote, "with reference to the pastoral priorities and in what concerns objective doctrinal difficulties, the Council texts show diversity of theological nuances which it is quite hard to harmonize."7 In a similar manner, with regard to the 1983 revision of the Code of Canon Law, the American canonist James Provost commented that there is:still no coherent treatment of the permanent deacons as a "proper and permanent rank in the hierarchy" comparable to the treatment given presbyters and bishops in the code; rather they are treated as exceptions to the norms for presbyters.8As a result, both before and after the Second Vatican Council, theological consideration of Holy Orders focused almost exclusively on the episcopate and presbyterate.9The recognition of a deficient theological development in the diaconate does not mean that there has been no progress over the centuries. There are, as Kerkvoorde observes, fragments throughout the Tradition up to and beyond the Vatican II. Moreover, there are some who have proposed new [End Page 1276] ways of envisioning the diaconate grounded in these very same fragments.10 While these have advanced our understanding of the diaconate as an order, missing is precisely how the three degrees relate to one another and how this unity is grounded.As the Catechism of the Catholic Church (CCC) points out, Holy Orders is a single sacrament consisting of three degrees. If one degree, say the diaconate, is theologically impoverished, then the unity of Holy Orders suffers from this same deficiency. Put another way, the triune nature of this sacrament means that its unity is dependent upon the three degrees and their relationship to one another. Commenting on this dependency, the English Dominican scholar Aidan Nichols observes: "The priesthood cannot be approached in isolation from the episcopate and the diaconate."11 To better illustrate the relationship of the three degrees to the intelligibility of Holy Orders, he goes on to observe:To the ordinary Catholic Christian, the priesthood is the order with which he or she is most familiar, and understandably so.... In this sense, it is the central image of the triptych: yet the central panel cannot be appreciated without those which flank it. We need the whole picture. 12The image of the triptych to describe the unity and diversity of Holy Orders is quite useful. As a work... (shrink)

The paper considers two-agent order acceptance scheduling problems with different scheduling criteria. Two agents have a set of jobs to be processed by a single machine. The processing time and due date of each job are known in advance. In the order accepting scheduling problem, jobs are allowed to be rejected. The objective of the problem is to maximize the net revenue while keeping the weighted number of tardy jobs for the second agent within a predetermined value. (...) A mixed-integer linear programming formulation is provided to obtain the optimal solution. The problem is considered as an NP-hard problem. Therefore, MILP can be used to solve small problem instances optimally. To solve the problem instances with realistic size, heuristic and metaheuristic algorithms have been proposed. A heuristic method is used to determine and secure a quick solution while the metaheuristic based on particle swarm optimization is designed to obtain the near-optimal solution. A numerical experiment is piloted and conducted on the benchmark instances that could be obtained from the literature. The performances of the proposed algorithms are tested through numerical experiments. The proposed PSO can obtain the solution within 0.1% of the optimal solution for problem instances up to 60 jobs. The performance of the proposed PSO is found to be significantly better than the performance of the heuristic. (shrink)

The central aim of the present investigation is to shed light on Nietzsche’s understanding of happiness and a good life, starting from Nietzsche’s appropriation of Plato’s and Aristotle’s doctrine of a hierarchy of human beings and forms of life.

Subjects exposed to strings of letters generated by a finite state grammar can later classify grammatical and nongrammatical test strings, even though they cannot adequately say what the rules of the grammar are (e.g., Reber, 1989). The MINERVA 2 (Hintzman, 1986) and Medin and Schaffer (1978) memory‐array models and a number of connectionist outoassociator models are tested against experimental data by deriving mainly parameter‐free predictions from the models of the rank order of classification difficulty of test strings. The (...) importance of different assumptions regarding the coding of features (How should the absence of a feature be coded? Should single letters or digrams be coded?), the learning rule used (Hebb rule vs. delta rule), and the connectivity (Should features be predicted only by previous features in the string, or by all features simultaneously?) is investigated by determining the performance of the models with and without each assumption. Only one class of connectionist model (the simultaneous delta rule) passes all the tests. It is shown that this class of model can be regarded by abstracting a set of representative but incomplete rules of the grammar. (shrink)

IntroductionThe pelvic floor muscles are active during motor tasks that increase intra-abdominal pressure, but little is known about how the PFM respond to dynamic activities, such as gait. The purpose of this study was to characterize and compare PFM activity during walking and jogging in continent adults across the entire gait cycle.Methods17 able-bodied individuals with no history of incontinence participated in this study. We recorded electromyography from the abdominal muscles, gluteus maximus, and PFM while participants performed attempted maximum voluntary contractions (...) of all muscles and completed 60–70 strides in four gait conditions: slow walk ; regular walk ; transition walk ; jog. We quantified activity throughout the whole gait cycle and during periods of bursting for each participant, and analyzed the timing of PFM bursting periods to explore when the PFM were most active in the gait cycle. We also conducted a phase metric analysis on the PFM and GM burst timings. We performed a Spearman's rank-order correlation to examine the effect of speed on %aMVCGC, %aMVCBR, and phase metric score, and used the Wilcoxon Signed-Rank test to evaluate the effect of gait modality, matched for speed, on these variables.ResultsThe PFM were active throughout the gait cycle, with bursts typically occurring during single-leg support. The PFM and GM were in phase for 44–69% of the gait cycle, depending on condition. There was a positive correlation between gait speed and both %aMVCGC and %aMVCBR. Phase metric scores were significantly higher during jogging than transition walking, but there was no difference between gait modality on %aMVCGC or %aMVCBR. Where possible we disaggregated data by sex, although were unable to make statistical comparisons due to low sample sizes.ConclusionThe PFM are active during walking and jogging, with greater activity at faster speeds and with bursts in activity around single-leg support. The PFM and GM co-activate during gait, but are not completely in phase with each other. (shrink)

We show that Mitchell order on downward closed extenders below rank-to-rank type is wellfounded.

In this paper we study elimination of imaginaries in some classes of pure ordered abelian groups. For the class of ordered abelian groups with bounded regular rank (equivalently with finite spines) we obtain weak elimination of imaginaries once we add sorts for the quotient groups $\Gamma /\Delta $ for each definable convex subgroup $\Delta $, and sorts for the quotient groups $\Gamma /(\Delta + \ell \Gamma )$ where $\Delta $ is a definable convex subgroup and $\ell \in \mathbb {N}_{\geq (...) 2}$. We refer to these sorts as the quotient sorts. For the dp-minimal case we obtain a complete elimination of imaginaries if we also add constants to distinguish the cosets of $\ell \Gamma $ in $\Gamma $, where $\ell \in \mathbb {N}_{\geq 2}$. (shrink)

O-minimal structures have long been thought to occupy the base of a hierarchy of ordered structures, in analogy with the role that strongly minimal structures play with respect to stable theories. This is the first in an anticipated series of papers whose aim is the development of model theory for ordered structures of rank greater than one. A class of ordered structures to which a notion of finite rank can be assigned, the decomposable structures, is introduced here. These (...) include all ordered structures definable in o-minimal structures. The principal result in this paper, Theorem 5.1, asserts roughly that a decomposable structure [Formula: see text] can be partitioned into finitely many definable subsets such that on each set the restriction of < is a "twisted lexicographic" order. As a consequence, for all n and linear orders ≺ definable on a subset X ⊆ Mn in an o-minimal structure [Formula: see text], there is a definable partition of X such that the restriction of ≺ to each set in the partition is "lexicographic". (shrink)

Dual-ranking act-consequentialism (DRAC) is a rather peculiar version of act-consequentialism. Unlike more traditional forms of act-consequentialism, DRAC doesn’t take the deontic status of an action to be a function of some evaluative ranking of outcomes. Rather, it takes the deontic status of an action to be a function of some non-evaluative ranking that is in turn a function of two auxiliary rankings that are evaluative. I argue that DRAC is promising in that it can accommodate certain features of commonsense morality (...) that no single-ranking version of act-consequentialism can: supererogation, agent-centered options, and the self-other asymmetry. I also defend DRAC against three objections: (1) that its dual-ranking structure is ad hoc, (2) that it denies (putatively implausibly) that it is always permissible to make self-sacrifices that don’t make things worse for others, and (3) that it violates certain axioms of expected utility theory, viz., transitivity and independence. (shrink)

We prove that the maximal order type of the wqo of linear orders of finite Hausdorff rank under embeddability is φ2, the first fixed point of the ε-function. We then show that Fraïssé’s conjecture restricted to linear orders of finite Hausdorff rank is provable in +“φ2 is well-ordered” and, over , implies +“φ2 is well-ordered”.

It is well-known that natural axiomatic theories are well-ordered by consistency strength. However, it is possible to construct descending chains of artificial theories with respect to consistency strength. We provide an explanation of this well-orderedness phenomenon by studying a coarsening of the consistency strength order, namely, the$\Pi ^1_1$reflection strength order. We prove that there are no descending sequences of$\Pi ^1_1$sound extensions of$\mathsf {ACA}_0$in this ordering. Accordingly, we can attach a rank in this order, which we call (...) reflection rank, to any$\Pi ^1_1$sound extension of$\mathsf {ACA}_0$. We prove that for any$\Pi ^1_1$sound theoryTextending$\mathsf {ACA}_0^+$, the reflection rank ofTequals the$\Pi ^1_1$proof-theoretic ordinal ofT. We also prove that the$\Pi ^1_1$proof-theoretic ordinal of$\alpha $iterated$\Pi ^1_1$reflection is$\varepsilon _\alpha $. Finally, we use our results to provide straightforward well-foundedness proofs of ordinal notation systems based on reflection principles. (shrink)

Rankings have dramatically proliferated over the past several decades. An often-overlooked impact of this proliferation is that it has facilitated the institutionalization of an imaginary of the modern world as a stratified order, whose actors are imagined as continuously striving to perform better than others. To better understand this impact, we need to take a closer look at rankings’ premises and the way these resonate with the broader institutional environment of which rankings are a part.

In traditional consequentialism the good is position-neutral. A single evaluative ranking of states of affairs is correct for everyone, everywhere regardless of their positions. Recently, position-relative forms of consequentialism have been developed. These allow for the correct rankings of states to depend on connections that hold between the state being evaluated and the position of the evaluator. For example, perhaps being an agent who acts in a certain state requires me to rank that state differently from someone else (...) who lacks this connection. In this chapter several different kinds of position-relative rankings related to agents, times, physical locations, and possible worlds are explored. Arguments for and against adopting a position-relative axiology are examined, and it is suggested that position-relative consequentialism is a promising moral theory that has been underestimated. (shrink)

Partial order optimality theory is a conservative generalization of classical optimality theory that makes possible the modeling of free variation and quantitative regularities without any numerical parameters. Solving the ranking problem for PoOT has so far remained an outstanding problem: allowing for free variation, given a finite set of input/output pairs, i.e., a dataset, \ that a speaker S knows to be part of some language L, how can S learn the set of all grammars G under some constraint (...) set C compatible with \?. Here, allowing for free variation, given the set of all PoOT grammars GPoOT over a constraint set C, for an arbitrary \, I provide set-theoretic means for constructing the actual set G compatible with \. Specifically, I determine the set of all STRICT ORDERS of C that are compatible with \. As every strict total order is a strict order, our solution is applicable in both PoOT and COT, showing that the ranking problem in COT is a special instance of a more general one in PoOT. (shrink)

The Spohnian paradigm of ranking functions is in many respects like an order-of-magnitude reverse of subjective probability theory. Unlike probabilities, however, ranking functions are only indirectly—via a pointwise ranking function on the underlying set of possibilities W —defined on a field of propositions A over W. This research note shows under which conditions ranking functions on a field of propositions A over W and rankings on a language L are induced by pointwise ranking functions on W and the set (...) of models for L, ModL, respectively. (shrink)

We study the class of elementary submodels of a large superstable homogeneous model. We introduce a rank which is bounded in the superstable case, and use it to define a dependence relation which shares many (but not all) of the properties of forking in the first order case. The main difference is that we do not have extension over all sets. We also present an example of Shelah showing that extension over all sets may not hold for any (...) dependence relation for superstable homogeneous models. (shrink)

Different evaluators typically disagree how to rank different candidates due to their idiosyncratic concerns for the various qualities of the candidates. Our ranking mechanism asks all evaluators to submit individual bids assigning a monetary amount for each possible rank order. The rules specify for all possible vectors of such individual bids the collectively binding rank order of candidates and the payments, due to the different evaluators. Three requirements uniquely determine procedurally fair ranking rules as a (...) game form. Only when additionally assuming exogenously given true evaluations of collective rankings, which may be commonly or only privately known, and—in case of private information—beliefs concerning the evaluations by others, this game form determines proper games and allows for equilibrium analysis. After an illustration, the approach is adjusted to situations where one wants to rank only acceptable sets of candidates thus rendering the mechanism even more attractive. (shrink)

We define some variations of the Scott rank for countable models and obtain some inequalities involving the ranks. For mono-unary algebras we prove that the game rank of any subtree does not exceed the game rank of the whole model. However, similar questions about linear orders remain unresolved.

We study the class of elementary submodels of a large superstable homogeneous model. We introduce a rank which is bounded in the superstable case, and use it to define a dependence relation which shares many (but not all) of the properties of forking in the first order case. The main difference is that we do not have extension over all sets. We also present an example of Shelah showing that extension over all sets may not hold for any (...) dependence relation for superstable homogeneous models. (shrink)

From 1827 to 1831 the German historian Leopold von Ranke travelled through Germany, Austria, and Italy, hunting for documents and archives. During this journey Ranke developed a new model for historical research that transformed the archive into the most important site for the production of historical knowledge. Within the archive, Ranke claimed, the trained historian could forget his personal predispositions and political loyalties, and write objective history. This essay critically examines Ranke's model for historical research through a study of the (...) obstacles, frustrations, and joys that he encountered on his journey. It shows how Ranke's archival experiences inspired him to re-evaluate his own identity as a historian and as a human being, and investigates some of the affiliations between his model for historical research and the political realities of Prince Metternich's European order. Finally, the essay compares Ranke's historical discipline to other nineteenth-century disciplines, such as anthropology and archaeology. (shrink)

In this paper, I investigate the relationship between preference and judgment aggregation, using the notion of ranking judgment introduced in List and Pettit. Ranking judgments were introduced in order to state the logical connections between the impossibility theorem of aggregating sets of judgments and Arrow’s theorem. I present a proof of the theorem concerning ranking judgments as a corollary of Arrow’s theorem, extending the translation between preferences and judgments defined in List and Pettit to the conditions on the aggregation (...) procedure. (shrink)

The study of classes of models of a finite diagram was initiated by S. Shelah in 1969. A diagram D is a set of types over the empty set, and the class of models of the diagram D consists of the models of T which omit all the types not in D. In this work, we introduce a natural dependence relation on the subsets of the models for the 0-stable case which share many of the formal properties of forking. This (...) is achieved by considering a rank for this framework which is bounded when the diagram D is 0-stable. We can also obtain pregeometries with respect to this dependence relation. The dependence relation is the natural one induced by the rank, and the pregeometries exist on the set of realizations of types of minimal rank. Finally, these concepts are used to generalize many of the classical results for models of a totally transcendental first-order theory. In fact, strong analogies arise: models are determined by their pregeometries or their relationship with their pregeometries; however the proofs are different, as we do not have compactness. This is illustrated with positive results as well as negative results . We also give a proof of a Two Cardinal Theorem for this context. (shrink)

In this paper, we introduce the notion of $${\textbf{K}} $$ -rank, where $${\textbf{K}} $$ is a strong amalgamation Fraïssé class. Roughly speaking, the $${\textbf{K}} $$ -rank of a partial type is the number “copies” of $${\textbf{K}} $$ that can be “independently coded” inside of the type. We study $${\textbf{K}} $$ -rank for specific examples of $${\textbf{K}} $$, including linear orders, equivalence relations, and graphs. We discuss the relationship of $${\textbf{K}} $$ -rank to other ranks in model (...) theory, including dp-rank and op-dimension (a notion coined by the first author and C. D. Hill in previous work). (shrink)

This work introduces the framework for selecting architecture in 5G networks, considering various technological, performance, economic, and operational factors. With the emergence of 5G technology, the architecture selection process has become pivotal in meeting diverse requirements for ultra-high-speed connectivity, low latency, scalability, and diverse service demands. The evaluation comprehensively analyses different architecture options, including centralized, distributed, cloud-based, and virtualized architectures. Factors such as network performance, scalability, cost-effectiveness, security, and compatibility are considered within a multi-criteria decision-making framework. Findings reveal each architecture (...) option's diverse strengths and limitations, emphasizing the importance of aligning architectural choices with specific use cases, deployment scenarios, and business objectives. We used the concept of multi-criteria decision-making (MCDM) methodology to control the various criteria. We used the single-valued neutrosophic set (SVNS) to deal with vague and inconsistent data. The SVNS is integrated with the hyperSoft set. The proposed methodology uses a single-valued neutrosophic hyperSoft set (SVNHSS) to select the best 5G architecture. We used the VIKOR method as an MCDM method to rank the alternatives. The proposed framework provides stakeholders with a structured methodology to evaluate and prioritize architecture options, facilitating informed decision-making in the complex landscape of 5G network deployments. (shrink)

The more we rely on digital assistants, online search engines, and AI systems to revise our system of beliefs and increase our body of knowledge, the less we are able to resort to some independent criterion, unrelated to further digital tools, in order to asses the epistemic reliability of the outputs delivered by them. This raises some important questions to epistemology in general and pressing questions to applied to epistemology in particular. In this paper, we propose an experimental method (...) for the assessment of GPT-3’s capacity to generate consistent and coherent sets of outputs. When several outputs to one and the same input are very repetitive they tend to be consistent with each other, that is they do not contradict each other. But consistency does not make the set of outputs as a whole more informative than the outputs considered individually. We argue that the less informative a set of outputs is, the less coherent it is. We establish a conceptual distinction between consistency and coherence in the light of what some epistemologists refer to as a coherence theories of truth and justification. While much attention has been given to GPT-3’s capacity to produce internally coherent individual outputs, we argue, instead, that more attention should be given to its capacity to produce consistent and coherent outputs generated on a single-input-multiple-outputs basis. (shrink)

Minimality ranks in the style of Deissler are one way of measuring the structural complexity of minimal extensions of first-order structures. In particular, positive Deissler rank measures the complexity of the injective envelope of a module as an extension of that module. In this paper we solve a problem of the second author by showing that certain injective envelopes have the maximum possible positive Deissler rank complexity. The proof shows that this complexity naturally reflects the internal structure (...) of the injective extension in the form of the levels of the Matlis hierarchy. (shrink)

We define an appropriate analog of the Morley rank in a totally transcendental homogeneous model with type diagram D. We show that if RM[p] = α then for some 1 ≤ n < ω the type p has n, but not n + 1, distinct D-extensions of rank α. This is surprising, because the proof of the statement in the first-order case depends heavily on compactness. We also show that types over (D,ℵ₀)-homogeneous models have multiplicity (Morley degree) (...) 1. (shrink)

While numerous studies have shown diverse effects of rankings, rather little is known about their production. This article contributes to a broader understanding of rankings in society, and does so by focusing on underlying worldviews. I argue that the existence of a ranking and its concrete methodology can be explained by the producer’s paradigmatic assumptions about a world-to-be-ranked. Referring to the sociology of knowledge and studies on commensuration, comparisons, quantification and valuation, I provide a general heuristic to analyze this relation (...) between underlying worldviews and observational regimes through which order is constructed systematically. Presenting empirical results on a ranking for the most famous artists in the world, I show how the review device’s initial problem and its construction of order derive from consistent assumptions about contemporary art, its symbolic structures and its social embeddedness. These findings have implications for both research on rankings and sociology of the arts. (shrink)