The bounded proper forcing axiom BPFA is the statement that for any family of ℵ 1 many maximal antichains of a proper forcing notion, each of size ℵ 1 , there is a directed set meeting all these antichains. A regular cardinal κ is called Σ 1 -reflecting, if for any regular cardinal χ, for all formulas $\varphi, "H(\chi) \models`\varphi'"$ implies " $\exists\delta . We investigate several algebraic consequences of BPFA, and we show that the consistency strength of the bounded (...) proper forcing axiom is exactly the existence of a Σ 1 -reflecting cardinal (which is less than the existence of a Mahlo cardinal). We also show that the question of the existence of isomorphisms between two structures can be reduced to the question of rigidity of a structure. (shrink)

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Model Theory in Logic and Philosophy of Logic

Philosophy of Mathematics

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We reimplement the creature forcing construction used by Fischer et al. :1045–1103, 2017. https://doi.org/10.1007/S00153-017-0553-8. arXiv:1402.0367 [math.LO]) to separate Cichoń’s diagram into five cardinals as a countable support product. Using the fact that it is of countable support, we augment our construction by adding uncountably many additional cardinal characteristics, sometimes referred to as localisation cardinals.

If ZFC is consistent, then each of the following is consistent with ZFC + 2ℵ0 = ℵ2: (1) $X \subseteq \mathbb{R}$ is of strong measure zero iff |X| ≤ ℵ1 + there is a generalized Sierpinski set. (2) The union of ℵ1 many strong measure zero sets is a strong measure zero set + there is a strong measure zero set of size ℵ2 + there is no Cohen real over L.

We use a creature construction to show that consistently $$\begin{aligned} \mathfrak d=\aleph _1= {{\mathrm{cov}}}< {{\mathrm{non}}}< {{\mathrm{non}}}< {{\mathrm{cof}}} < 2^{\aleph _0}. \end{aligned}$$The same method shows the consistency of $$\begin{aligned} \mathfrak d=\aleph _1= {{\mathrm{cov}}}< {{\mathrm{non}}}< {{\mathrm{non}}}< {{\mathrm{cof}}} < 2^{\aleph _0}. \end{aligned}$$.

We give a self-contained proof of the preservation theorem for proper countable support iterations known as “tools-preservation”, “Case A” or “first preservation theorem” in the literature. We do not assume that the forcings add reals.

1. If A is strongly amorphous , then its power set P is dually Dedekind infinite, i. e., every function from P onto P is injective. 2. The class of “inexhaustible” sets is not closed under supersets unless AC holds.

We investigate the Ramsey theory of continuous graph-structures on complete, separable metric spaces and apply the results to the problem of covering a plane by functions. Let the homogeneity number[Formula: see text] of a pair-coloring c:[X]2→2 be the number of c-homogeneous subsets of X needed to cover X. We isolate two continuous pair-colorings on the Cantor space 2ω, c min and c max, which satisfy [Formula: see text] and prove: Theorem. For every Polish space X and every continuous pair-coloringc:[X]2→2with[Formula: see (...) text], [Formula: see text] There is a model of set theory in which[Formula: see text]and[Formula: see text]. The consistency of [Formula: see text] and of [Formula: see text] follows from [20]. We prove that [Formula: see text] is equal to the covering number of 2 by graphs of Lipschitz functions and their reflections on the diagonal. An iteration of an optimal forcing notion associated to c min gives: Theorem. There is a model of set theory in which ℝ2 is coverable byℵ1graphs and reflections of graphs of continuous real functions; ℝ2 is not coverable byℵ1graphs and reflections of graphs of Lipschitz real functions. Figure 1.1 in the introduction summarizes the ZFC results in Part I of the paper. The independence results in Part II show that any two rows in Fig. 1.1 can be separated if one excludes [Formula: see text] from row. (shrink)

We investigate the behavior of cardinal characteristics of the reals under extensions that do not add new [Formula: see text]-sequences (for some regular [Formula: see text]). As an application, we show that consistently the following cardinal characteristics can be different: The (“independent”) characteristics in Cichoń’s diagram, plus [Formula: see text]. (So we get thirteen different values, including [Formula: see text] and continuum). We also give constructions to alternatively separate other MA-numbers (instead of [Formula: see text]), namely: MA for [Formula: see (...) text]-Knaster from MA for [Formula: see text]-Knaster; and MA for the union of all [Formula: see text]-Knaster forcings from MA for precaliber. (shrink)

We investigate the behavior of cardinal characteristics of the reals under extensions that do not add new <κ-sequences. As an application, we show that consistently the followi...

Reviewed Works:Tomek Bartoszynski, Marion Scheepers, Set Theory, Annual Boise Extravaganza in Set Theory Conference, March 13-15, 1992, April 10-11, 1993, March 25-27, 1994, Boise State University, Boise, Idaho.R. Aharoni, A. Hajnal, E. C. Milner, Interval Covers of a Linearly Ordered Set.Eyal Amir, Haim Judah, Souslin Absoluteness, Uniformization and Regularity Properties of Projective Sets.Tomek Bartoszynski, Ireneusz Reclaw, Not Every $\gamma$-Set is Strongly Meager.Andreas Blass, Reductions Between Cardinal Characteristics of the Continuum.Claude Laflamme, Filter Games and Combinatorial Properties of Strategies.R. Daniel Mauldin, Analytic (...) non-Borel Sets Modulo Null Sets.Janusz Pawlikowski, Laver's Forcing and Outer Measure.Marion Scheepers, Meager Sets and Infinite Games.Saharon Shelah, On Some Problems in General Topology.Saharon Shelah, Remarks on $\aleph_1$-CWH not CWH First Countable Spaces.Juris Steprans, Cardinal Invariants Associated with Hausdorff Capacities. (shrink)

Online supplement, "Mulsow: Additions to Notes drawn from the 2002 edition of Moderne aus dem Untergrund" full versions of nearly 300 notes that were truncated in the print edition. Hosted on H. C. Erik Midelfort's website. Martin Mulsow's seismic reinterpretation of the origins of the Enlightenment in Germany won awards and renown in its original German edition, and now H. C. Erik Midelfort's translation makes this sensational book available to English-speaking readers. In Enlightenment Underground, Mulsow shows that even in (...) the late seventeenth century some thinkers in Germany ventured to express extremely dangerous ideas, but did so as part of a secret underground. Scouring manuscript collections across northern Europe, Mulsow studied the writings of countless hitherto unknown radical jurists, theologians, historians, and dissident students who pushed for the secularization of legal, political, social, and religious knowledge. Often their works circulated in manuscript, anonymously, or as clandestinely published books. Working as a philosophical microhistorian, Mulsow has discovered the identities of several covert radicals and linked them to circles of young German scholars, many of whom were connected with the vibrant radical cultures of the Netherlands, England, and Denmark. The author reveals how radical ideas and contributions to intellectual doubt came from Socinians and Jews, church historians and biblical scholars, political theorists, and unemployed university students. He shows that misreadings of humorous or ironic works sometimes gave rise to unintended skeptical thoughts or corrosively political interpretations of Christianity. This landmark book overturns stereotypical views of the early Enlightenment in Germany as cautious, conservative, and moderate, and replaces them with a new portrait that reveals a movement far more radical, unintended, and puzzling than previously suspected. (shrink)

We show that it is consistent that the reaping number r is less than u , the size of the smallest base for an ultrafilter. To show that our forcing preserves certain ultrafilters, we prove a general partition theorem involving Ramsey ideals.

This collection of texts (originally published in German under the title Holzwege) is Heidegger's first post-war book and contains some of the major expositions of his later philosophy. Of particular note are 'The Origin of the Work of Art', perhaps the most discussed of all of Heidegger's essays, and 'Nietzsche's Word 'God is Dead',' which sums up a decade of Nietzsche research. Although translations of the essays have appeared individually in a variety of places, this is the first English translation (...) to bring them all together as Heidegger intended. The text is taken from the last edition of the work, which contains the author's final corrections together with important marginal annotations that provide considerable insight into the development of his thought. This fresh and accurate new translation will be an invaluable resource for all students of Heidegger, whether they work in philosophy, literary theory, religious studies, or intellectual history. (shrink)

Explores the moral dimensions of the current global role of the U.S. military.

Christian Georg Martin offers an argumentative reconstruction of the whole work, reading it as a critical ontology, namely as the attempt to abstract from all presuppositions and to immanently unfold conceptual determinations characterizing ...

And, as The Promise of Salvation makes clear through abundant empirical evidence, religion will not disappear as long as these promises continue to help people ...

Bd. 1. A-B -- Bd. 2. C-F -- Bd. 3. G-Inn -- Bd. 4. Ins-Loc.

The aim of this paper is to provide a proof-theoretic characterization of relevant logics including fusion and fission connectives, as well as Ackermann’s truth constant. We achieve this by employing the well-established methodology of labelled sequent calculi. After having introduced several systems, we will conduct a detailed proof-theoretic analysis, show a cut-admissibility theorem, and establish soundness and completeness. The paper ends with a discussion that contextualizes our current work within the broader landscape of the proof theory of relevant logics.

Classic text considersgeneral theory of computability, computable functions, operations on computable functions, Turing machines self-applied, unsolvable decision problems, applications of general theory, mathematical logic, Kleene hierarchy, computable functionals, classification of unsolvable decision problems and more.

Martin Heidegger's Contributions to Philosophy reflects his famous philosophical "turning." In this work, Heidegger returns to the question of being from its inception in Being and Time to a new questioning of being as event.

Background Neuroimaging and lesion studies suggested that the dorsolateral prefrontal and posterior parietal cortices mediate visual metacognitive awareness. The causal evidence provided by non-invasive brain stimulation, however, is inconsistent. -/- Objective/hypothesis Here we revisit a major figure discrimination experiment adding a new Kanizsa figure task trying to resolve whether bilateral continuous theta-burst transcranial magnetic stimulation (cTBS) over these regions affects perceptual metacognition. Specifically, we tested whether subjective visibility ratings and/or metacognitive efficiency are lower when cTBS is applied to these two (...) regions in comparison to an active control region. -/- Methods A within-subjects design including three sessions spaced by one-week intervals was implemented. In each session, every participant was administered bilateral cTBS to either prefrontal, control or parietal cortices. Two concurrent tasks were performed, a real and an illusory figure task, stabilising objective performance with use of an adaptive staircase procedure. -/- Results When performing the replicated task, cTBS was found insufficient to disrupt neither visibility ratings nor metacognitive efficiency. However, with use of Kanizsa style illusory figures, cTBS over the dorsolateral prefrontal, but not over the posterior parietal cortex, was observed to significantly diminish metacognitive efficiency. -/- Conclusion(s) Real and illusory figure tasks demonstrated different cTBS effects. A possible explanation is the involvement of the prefrontal cortex in the creation of expectations, which is necessary for efficient metacognition. Failure to replicate previous findings for the real figure task, however, cannot be said to support, conclusively, the notion that these brain regions have a causal role in metacognitive awareness. This inconsistent finding may result from certain limitations of our study, thereby suggesting the need for yet further investigation. (shrink)

In their 2010 book, Biology’s First Law, D. McShea and R. Brandon present a principle that they call ‘‘ZFEL,’’ the zero force evolutionary law. ZFEL says (roughly) that when there are no evolutionary forces acting on a population, the population’s complexity (i.e., how diverse its member organisms are) will increase. Here we develop criticisms of ZFEL and describe a different law of evolution; it says that diversity and complexity do not change when there are no evolutionary causes.

We provide a battery of examples of delusions against which theoretical accounts can be tested. Then, we identify neuropsychological anomalies that could produce the unusual experiences that may lead, in turn, to the delusions in our battery. However, we argue against Maher’s view that delusions are false beliefs that arise as normal responses to anomalous experiences. We propose, instead, that a second factor is required to account for the transition from unusual experience to delusional belief. The second factor in the (...) aetiology of delusions can be described superficially as a loss of the ability to reject a candidate for belief on the grounds of its implausibility and its inconsistency with everything else that the patient knows. But we point out some problems that confront any attempt to say more about the nature of this second factor. (shrink)

If the tiles of a mosaic are arranged symmetrically, then the image those tiles constitute must be symmetric as well. This paper formulates and defends the general principle at work in this case: roughly, that a symmetry cannot ground an asymmetry. It is argued that the principle supports strong objections to four metaphysical views: qualitativism, relationalism, the tenseless or ‘B’ theory of time, and comparativism. A response to these objections is developed which appeals to fragmentalism, the view that reality contains (...) facts which are incompatible with one another. But fragmentalism might be thought too bizarre to tolerate, and if it is, then the objections developed in this paper may well be fatal. (shrink)

Taking issue with those who see recent social transformations as an extension of modernity, the author contends that social theory must confront an epochal change from the modern era to a new era of globality, in which human beings can conceive of forces at work on a global scale, and in which they espouse values that take the globe as their reference point. The book begins by assessing the problems of writing about modernity, showing how narratives of an endlessly self-perpetuating (...) modern age were intrinsic to the "modern project," the attempt by Enlightenment philosophers to transform the everyday world in accord with science and logic under the auspices of the nation-state. Now we are beginning to realize that the nation-state and the modern project cannot renew themselves endlessly through expansion. Instead, the author contends, the age has culminated in its own dissolution, and globality has supplanted modernity as the basis for action and social organization. In theorizing the global age, he considers the worldwide environmental consequences of aggregate human activities, the reconception of human security in the age of nuclear weapons, technological advances in communication systems, the rise of a global economy, and the growing reflexivity of global consciousness, as people and groups begin to refer to the globe as the frame for their beliefs. The book concludes by examining the consequences of the Global Age thesis for politics, identifying a new popular construction of the state that the author terms "performative citizenship." In the modern age, the nation-state was the central power and citizens were beneficiaries of that power, with rights and duties. In the global age, citizens respond to the lack of central power by creating, or performing, the state themselves. The global managerial class uses the skills learned in the bureaucracy of the nation-state to bring pressure on national governments in the interests of global economic, environmental, or human-rights issues. (shrink)

Article copyright 2002. We provide a battery of examples of delusions against which theoretical accounts can be tested. Then we identify neuropsychological anomalies that could produce the unusual experiences that may lead, in turn, to the delusions in our battery. However, we argue against Maher's view that delusions are false beliefs that arise as normal responses to anomalous experiences. We propose, instead, that a second factor is required to account for the transition from unusual experience to delusional belief. The second (...) factor in the etiology of delusions can be described superficially as a loss of the ability to reject a candidate for belief on the grounds of its implausibility and its inconsistency with everything else that the patient knows, but we point out some problems that confront any attempt to say more about the nature of this second factor. (shrink)

Butz, Achimova, Bilkey, and Knott provide a topic overview and discuss whether the special issue contributions may imply that event‐predictive abilities constitute a root for conceptual human thought, because they enable complex, mutually beneficial, but also intricately competitive, social interactions and language communication.

In his paper ‘Scmantic Theory and Tacit Knowlcdgc’, Gareth Evans uscs a familiar kind of cxamplc in ordcr to render vivid his account of tacit knowledge. We arc to consider a finite language, with just one hundrcd scntcnccs. Each scntcncc is made up of a subjcct (a name) and a prcdicatc. The names are ‘a’, ‘b’, . . ., T. The prcdicatcs arc ‘F’, ‘G’, . . ., ‘O’. Thc scntcnccs have meanings which dcpcnd in a systematic way upon their (...) construction. Thus, all scntcnccs containing ‘a’ mean something about john; all scntcnccs containing ‘b’ mean something about Harry; all scntcnccs containing ‘F’ mean something about being bald; all scntcnccs containing ‘G’ mean something about being happy; and so 011. For this vcry simple language L, wc arc to consider various semantic theories. We could consider thcorics whosc dclivcranccs about wholc scntcnccs are of.. (shrink)

We apply Hrushovski-Fraïssé's amalgamation procedure to obtain a theory of fields of prime characteristic of Morley rank 2 equipped with a definable additive subgroup of rank 1.

Entrepreneurship education is increasingly becoming a focal strategy for promoting entrepreneurship, particularly to foster entrepreneurial intentions and startups. However, learning and support are equally important after startup for novice entrepreneurs to gain a good level of confidence to manage their business and achieve the desired outcomes. Using a sample of 189 young self-employed individuals in Uganda, this study examines the differential impact of mentoring and self-efficacy on the achievement of intangible outcomes of entrepreneurship including satisfaction of need for autonomy, work (...) satisfaction and the intention to stay in self-employment. We found self-efficacy to mediate the effects of mentoring on these intangible outcomes. In addition, the results showed substantial gender differences. Whereas women’s satisfaction of the need for autonomy and intention to stay in self-employment were strongly associated with the direct effects of mentoring, their male counterparts seemed to benefit more if mentoring resulted in increased self-efficacy. Overall, our findings suggest that whereas mentoring improves the competence of small business owners and consequently achievement of superior outcomes, mentoring should also focus on boosting self-efficacy which in turn is essential for the application of the entrepreneurial competencies. (shrink)

To assess the merits and demerits of the content of Culp’s educational programme, the paper does three things: First, it discusses whether Culp’s defence against conceivable objections manages to effectively dispel the charge of cosmopolitan arrogance. Second, it spells out one implication of epistemic modesty, which Culp considers a core competence to be imparted by citizenship education. Third, it reflects upon the tricky task of motivating individuals to comply with the demands of justice. Taken together, the paper argues that Culp’s (...) case is impressively strong but nevertheless tends to suffer from a rationalist constriction. It does not leave sufficient room for tradition in private life and public reasoning. This rationalist constriction is problematic from a normative philosophical, and especially a practice-oriented viewpoint. (shrink)