Infertility specialists may be confronted with the ethical dilemma of whether to disclose misattributed paternity (MP). Physicians should be prepared for instances when an assumed father’s evaluation reveals a condition known for lifelong infertility, for example, congenital bilateral absence of vas deferens (CBAVD). When there is doubt regarding a patient’s comprehension of his diagnosis, physicians must consider whether further disclosure is warranted. This article describes a case of MP with ethics analysis that concludes that limited nondisclosure is most consistent with (...) a physician’s principled duties to inform, to respect patients’ autonomy, and to employ nonmaleficence (including the avoidance of psychosocial harms). (shrink)

Respected modern scholars regard the pre-Buddhist philosopher Sañjaya Belaṭṭhiputta—a significant figure in the Buddhist canon—as the originator of the important classical argument- forms known as the catuṣkoṭi and catuṣkoṭi vinirmukta. We argue that the early Buddhist texts do not in fact support this view of the origin of these argument-forms; the question of their origin is open. While it is certainly true that the Pāli Sāmaññaphala Sutta and some of its parallels portray Sañjaya as deploying the catuṣkoṭi, there is nothing (...) in these passages to suggest that he was its originator. The situation concerning the catuṣkoṭi vinirmukta is perhaps even more surprising: There is nothing in the early Pāli texts and their parallels—nor in Buddhagosa’s famous Pāli commentary on the early texts—to show that Sañjaya even deployed the catuṣkoṭi vinirmukta let alone originated it. Further, our investigations also call into question the standard portrayal of Sañjaya as an obfuscator and prevaricator. It appears he may have been a more interesting and able philosopher than the Sāmaññaphala Sutta—and modern accounts based on it—maintain. (shrink)

Heidegger’s reading of Kant is deciphered to have illuminated his own project concerning the basic question of Ontology, Time, Space and History [Temporality, Spatiality and Historicity] embodying the novel description of Human reality in terms of Mit-Dasein and Mit-welt [Subjectivity with the public face]. Kant’s Critique of Pure Reason led Heidegger develop his own project of Existential Phenomenology contrary to Husserilian Phenomenology. We will discuss the Kantian Heidegger following the two main issues: one, Heidegger appreciates Kant on his identifying and (...) exploring the difference of ontic/ontological. Two, Kant prioritizes time over space. Heidegger would explore the subject of ontic/ontological difference in the sense that ontic knowledge is the knowledge of particular beings, whereas ontological knowledge is described as the a priori condition inferring the ontic knowledge. In this sense ontological knowledge pertains to question of being rather than beings. This is how Heidegger’s Kant interpretation would differ from the Neo-Kantianism of Marburg School which argued that Critique of Pure Reason is a work of epistemology. In contrast to this position, Heidegger held that Critique is a unique work of transcendental philosophy; it is theory of ontological knowledge but not ontic knowledge. Ontic knowledge of beings must conform to Being of beings [ontological foundation]. Heidegger holds that this should be Kant’s “Copernican Revolution”. However, Heidegger would appropriate the Kantian notion of time in the form of temporality of Dasein. Being manifests itself on beings through Being-there [Human reality] who purely understands Being. For Heidegger, temporality of Dasein is the foundation of ontological knowledge indeed. (shrink)

While a corporate ethics program is expected to reduce employees’ unethical behavior, understanding the effects of the ethics program elements on reducing the unethical behavior is a crucial issue. This study aims to explore how a corporate ethics program with multiple control elements, including punishment, monitoring, internal reporting, code of ethics, ethics support service and ethics training, influence employees’ threat appraisal process, coping appraisal process and unethical behavior at workplaces. The data to verify proposed research hypotheses were collected by administering (...) questionnaire survey on four autonomous government organizations in Bangladesh. Research findings show that only punishment and monitoring have significantly negative relationships with unethical behavior. Monitoring and internal reporting have significantly positive relationships with threat appraisal. The code of ethics, ethics support service and ethics training are associated positively with coping appraisal. The mediation results reveal that coping appraisal mediates the relationship between ethics program elements and unethical behavior; but the mediation effects of threat appraisal are not significant. This study provides valuable insights into how a corporate ethics program with multiple control elements reduces employees’ unethical behavior as well as how employees’ threat and coping appraisal processes are related to the corporate ethics program and unethical behavior in organizations. (shrink)

AimThe aim of this study was to determine the presence of depressive symptoms and understand the potential factors associated with these symptoms among physicians in Bangladesh during the COVID-19 pandemic.MethodsA cross-sectional study using an online survey was conducted in between April 21 and May 10, 2020, among physicians living in Bangladesh. Participants completed a series of demographic questions, COVID-19-related questions, and the Patient Health Questionnaire-9. Descriptive statistics, test statistics were performed to explore the association between physicians’ experience of depression symptoms (...) and other study variables. Stepwise binary logistic regression was followed while conducting the multivariable analysis.ResultA total of 390 physicians completed the survey. Of them, 283 were found to be experiencing depressive symptoms. Predictors which were significantly associated with depressive symptoms were gender, the presence of sleep disturbance, being highly exposed to media coverage about the pandemic, and fear around COVID-19 infection, being assaulted/humiliated by regulatory forces and by the general public, while traveling to and from the hospital and treating patients during the countrywide lockdown.ConclusionThe findings of this study demonstrate that there is a high prevalence of depressive symptom among physicians especially among female physicians in Bangladesh during the COVID-19 pandemic. Immediate, adequate and effective interventions addressing gender specific needs are required amid this ongoing crisis and beyond. (shrink)

Nanotechnology presents significant challenges in terms of developing a regulatory framework. This is due to a lack of scientific knowledge about the behaviour of the technology in its interactions with biological and ecological processes, the environment and other technologies. Crucially, there is a great deal of uncertainty surrounding the potential environmental and human health and safety impacts of NT. Consequently, the development of NT is a potential test case for framing new models of ‘soft law’ voluntary governance as a substitute (...) for traditional command and control type regulation. Driven by ‘new science governance,’ an approach based on a combination of ideas in anticipatory ethics, future-oriented responsibility, upstream public engagement and deliberation and theories of justice may offer a solution. The uniqueness of the approach can be found in the incorporation of anticipatory approaches via public participation and deliberation as the input into procedural justice approaches with distributional justice as the output. The overarching objective of this work is to contribute to the discussion in relation to the internalisation of responsibility and the building of intellectual and societal capacity to anticipate negative consequences before they arise in the hope that such an approach could be the antithesis of the retrospective imposition of responsibility and liability after the harm is done, which is the outcome of traditional regulatory and ethical approaches. Ultimately, the purpose is to contribute to the long-term sustainability of NT. (shrink)

This study addresses the critical shortage of parallel corpora for the Kashmiri language, a significant barrier to advancing language processing technologies for under-resourced languages. Despite Kashmiri's rich cultural heritage, the development of language technology resources, especially parallel corpora, has been notably limited. Our research involves a detailed analysis of the only available parallel corpora for Kashmiri, utilizing these datasets to develop and evaluate Neural Machine Translation (NMT) models. Through this evaluation, we categorize errors and assess the corpora's adequacy in quality (...) and quantity for supporting effective language processing tasks. Additionally, we investigate the reasons behind the scarcity of high-quality resources and identify the challenges inherent in creating robust parallel corpora for Kashmiri. By proposing solutions to these challenges, our study aims to contribute to the revitalization and global recognition of the Kashmiri language, bridging a significant gap in the field of language technology and emphasizing the importance of parallel corpora in preserving linguistic diversity and facilitating technological advancement. (shrink)

This article presents a theory of how the consumption of Islamic products may promote morally consistent behavior over time. We identify and examine three unique meta-characteristics (MCs) of Islamic ethics: ubudiyah (subservience to God), akhirah (focus on the hereafter or the long-term), and tawado (being modest while doing an ethical act). In four experiments, we show that after consumption of an Islamic banking product, MCs produce moral consistency or repeat ethical behavior, which is one major objective of an ethical system. (...) We also show that the absence of MCs results in moral inconsistency, that is, unethical behavior follows earlier consumption of an Islamic banking product due to the mediating psychological mechanism of moral licensing. Hence, it is not only the enactment of general ethical practices, rather the enactment of ethical practices in the specific context set by the MCs through which Islamic ethical system promotes ethical conduct and prevents unethical conduct. The findings have implications for Islamic ethical system and Islamic banking. (shrink)

The Holy Qur’an relates believers’ pure emotions to brotherhood. From the perspective of Islam, it has been also affirmed that two people have the same thoughts and opinions in one centre point of love in brotherhood, so fraternal feelings are not merely limited to kinship and consanguinity. In this line, the Holy Qur’an states that we have come to make you brothers with each other; not a brotherhood from parents, but an Islamic one, which is highly appreciated in the Islamic (...) society. In addition, a believing brother can never be filled when his fellow believer is hungry, and he cannot be clothed while the other is with nothing on. Islam further considers all Muslims as one family and calls everyone brothers and sisters or siblings. The true Muslims of any race and tribe as well as any language and age thus have a deep sense of brotherhood with each other, even if one lives in the Eastern parts of the world and the other in the West. In sum, this article aimed to investigate the role of religious teachings in strengthening believers’ brotherhood in the Islamic society. For this purpose, firstly, the definition of religious brotherhood was provided; secondly, religious brotherhood has been described based on the Holy Qur’an.Contribution: This article helped gain a new insight into the role of Islamic teachings in strengthening religious brotherhood in the Islamic society. Besides, the indicators of religious brotherhood were extracted and then enlightened according to the Ayat (viz. verses) from the Holy Qur’an. (shrink)

A review of economic thought since the sixteenth century reveals two streams of economic discourse, dirigisme and laissez-faire. Starting with the mercantilists, dirigiste approaches to economics embrace the real-world complexity of commodities that often differ greatly in attributes that are growth- and rent- augmenting. Most importantly, this means that free trade is likely to be polarising: it concentrates growth- and rent-augmenting commodities in countries that already enjoy a head start in these commodities. Advanced countries, therefore, support laissez-faire, while lagging countries (...) tend to support dirigisme. In order to rationalise their laissez-faire stance, advanced countries began developing a new economic discourse that strips commodities of their complexity. The foundations for this ideological reconstruction of economics were first laid by Adam Smith; this process eventually reached its climax with the neoclassical economists who stripped commodities down to one attribute: their capital intensity. In opposition to this laissez-faire economics, other writers, supportive of the interests of lagging countries, brought complexity back into their economic discourse; they argued that lagging countries had a fighting chance of catching up to advanced economies only by indigenising a growing array of growth- and rent-augmenting commodities. (shrink)

BackgroundOrgan donation has become one of the most effective ways to save lives and improve the quality of life for patients with end-stage organ failure. No previous studies have investigated the preferences for the different consenting options for organ donation in Egypt. This study aims to assess Egyptians’ preferences regarding consenting options for posthumous organ donation, and measure their awareness and acceptance of the Egyptian law articles regulating organ donation.MethodsA cross sectional study was conducted among 2743 participants over two years. (...) Each participant was required to rank eleven consenting options from 1 to 11, and to report his awareness and acceptance of the seven articles of the Egyptian law of organ donation.Results47% of the participants expressed willingness to donate their organs after death. This percentage increased to 78% when consenting options were explained to participants. “Informed consent by donor only” was the most preferred type of consent for one third of respondents. Awareness of the law articles regulating organ donation was relatively low ranging from 56% to 23%.ConclusionCurrently, around half of the Egyptian population agree to posthumous organ donation. This percentage could be increased significantly by raising the awareness about how the process of donation could be regulated and how the patient’s right of decision could be protected. (shrink)

Rehabilitation for disabled children requires long-term programmeswhich are expensive to the family. This study aimed to estimate the costincurred by caregivers’ children with disabilities from Pahang, Terengganu andKelantan participating in Community-Based Rehabilitation and cost of seeking alternative rehabilitation. Costanalysis using the Activity-Based Costing method was used to estimatetwelve-months’ expenditure in 2014 institutional year on 297 caregivers ofchildren with disability, aged 0 to 18 years who attended CBR. Data werecollected using a self-administered costing questionnaire and presentedin median. Results showed that the (...) median direct and indirect costs,excluding medications and alternative care were nearly four times as highin Home-Based compared to Centre-Based vs. RM608. Both groups of caregivers spent a significant amount ofresources on alternative rehabilitation. The high costs incurred for alternativerehabilitation is a major economic burden to the family. (shrink)

Informed consent to medical intervention is fundamental in both ethics and law. But in practice it is often not taken seriously in developing countries. This paper provides an appraisal of informed consent practices in Bangladesh. Following a review of the ethical and legal principles of informed consent, it assesses the degree to which doctors adhere to it in Bangladesh. Based on findings of non-compliance, it then investigates the reasons for such non-compliance through an appraisal of informed consent practices in Bangladesh (...) and provides recommendations aimed at improving such practices. The significance of this paper lies in unveiling the interdependence between the ethical and legal traits of informed consent and their ramifications on strengthening the patient-oriented approach of duty to care. (shrink)

The problem of finite-time stability of switched genetic regulatory networks with time-varying delays via Wirtinger’s integral inequality is addressed in this study. A novel Lyapunov–Krasovskii functional is proposed to capture the dynamical characteristic of GRNs. Using Wirtinger’s integral inequality, reciprocally convex combination technique and the average dwell time method conditions in the form of linear matrix inequalities are established for finite-time stability of switched GRNs. The applicability of the developed finite-time stability conditions is validated by numerical results.

This study concentrates on adaptive event-triggered control of complex dynamical networks with unpredictable coupling delays and stochastic deception attacks. The adaptive event-triggered mechanism is used to avoid the wasting of limited bandwidth. The probability of data communicated by the network is established by statistical properties and Bernoulli stochastic variables with an uncertain occurrence probability. Stability analysis based on Lyapunov–Krasovskii functional and the stability of the closed-loop system is guaranteed. Using the LMI technique, we obtain triggered parameters. To demonstrate the feasibility (...) and usefulness of the suggested methodology, two examples are shown. (shrink)

An attempt has been made to find some valuable information for particle detection with the help of Solid State Nuclear Track Detectors. The detector is characterized by a critical value of the energy-loss rate by the charged particle. Only those charged particles which give up energy exceeding the critical value alone can produce teachable tracks. The detection thresholds of nuclear track detectors can be specified in terms of their energy loss rates. The findings have been found within a good agreement (...) with the other works. (shrink)

The big five personality traits and entrepreneurial mindset are crucial individual-level elements that determine entrepreneurial intention. This study examines the impact of big five personality traits and EM, on EI using the theory of planned behavior. Besides, this study examined the role of entrepreneurial self-efficacy and attitude toward entrepreneurship influences EI. To achieve the research objectives, a quantitative approach was used. Structural equation modeling and path analysis were conducted using SmartPLS software. Data were collected from 270 respondents through online questionnaires. (...) Findings of the study revealed that big five personality traits influence ESE and ATE which led to EI. Finally, the moderating role of entrepreneurial passion was also found to have strong effect on influence ESE and ATE. This study offers evidence and insights that academics, educators, and others involved in the creation or expansion of entrepreneurial knowledge can use as a reference point. (shrink)

Background. Imposter syndrome, associated with self-doubt and fear despite clear accomplishments and competencies, is frequently detected in medical students and has a negative impact on their well-being. This study aimed to predict the students’ IS using the machine learning ensemble approach. Methods. This study was a cross-sectional design among medical students in Bangladesh. Data were collected from February to July 2020 through snowball sampling technique across medical colleges in Bangladesh. In this study, we employed three different machine learning techniques such (...) as neural network, random forest, and ensemble learning to compare the accuracy of prediction of the IS. Results. In total, 500 students completed the questionnaire. We used the YIS scale to determine the presence of IS among medical students. The ensemble model has the highest accuracy of this predictive model, with 96.4%, while the individual accuracy of random forest and neural network is 93.5% and 96.3%, respectively. We used different performance matrices to compare the results of the models. Finally, we compared feature importance scores between neural network and random forest model. The top feature of the neural network model is Y7, and the top feature of the random forest model is Y2, which is second among the top features of the neural network model. Conclusions. Imposter syndrome is an emerging mental illness in Bangladesh and requires the immediate attention of researchers. For instance, in order to reduce the impact of IS, identifying key factors responsible for IS is an important step. Machine learning methods can be employed to identify the potential sources responsible for IS. Similarly, determining how each factor contributes to the IS condition among medical students could be a potential future direction. (shrink)

Errors have been the concern of providers and consumers of health care services. However, consumers' perception of medical errors in developing countries is rarely explored. The aim of this study is to assess community members' perceptions about medical errors and to analyse the factors affecting this perception in one Middle East country, Oman.

With the development of wireless technology, two basic wireless network models that are commonly used, known as infrastructure and wireless ad hoc networks, have been developed. In the literature, it has been observed that channel contention is one of the main reasons for packet drop in WANETs. To handle this problem, this paper presents a routing protocol named CCBR. CCBR tries to determine a least contended path between the endpoints to increase packet delivery ratio and to reduce packet delay and (...) normalized routing overhead. Moreover, throughout the active data section, each intermediate node computes its channel contention value. If an intermediate node detects an increase in channel contention, it notifies the source node. Then the source node determines another least contended route for transmission. The advantages of CCBR are verified in our NS2-based performance study, and the results show that CCBR outperforms ad hoc on-demand distance vector in terms of packet delivery ratio, end-to-end delay, and routing overhead by 4% to 9%. (shrink)

The Canadian residential sector contributes approximately 80 megatons of GHGs to the environment yearly. With the ratification of Kyoto Protocol, Canada has committed to reduce its 1990 GHG emission levels by at least 5% between 2008 and 2012. To meet this target, Canada must evaluate and exploit all feasible means to reduce fossil fuel energy consumption and GHG emissions. Test-case Canadian houses were modeled in the building-energy simulation software ESP-r. Requisite housing stock data were extracted from Canada's residential end-use energy (...) surveys. Photovoltaic and wind-turbine energy systems were assessed for their contribution to electricity generation and GHG savings. Typical household electrical consumption versus renewable electricity generation was assessed to estimate the GHG reduction, cost saving in electricity, and the impact of these technologies on single detached houses. With the use of net-metering, 100% of electricity requirements can be met by these technologies in certain cases, resulting in significant reductions in GHG emissions. (shrink)

We present here an approach to the fine structure of L based solely on elementary model theoretic ideas, and illustrate its use in a proof of Global Square in L. We thereby avoid the Lévy hierarchy of formulas and the subtleties of master codes and projecta, introduced by Jensen [3] in the original form of the theory. Our theory could appropriately be called ”Hyperfine Structure Theory”, as we make use of a hierarchy of structures and hull operations which refines the (...) traditional Lα -or Jα-sequences with their Σn-hull operations.§1. Introduction. In 1938, K. Gödel defined the model L of set theory to show the relative consistency of Cantor's Continuum Hypothesis. L is defined as a unionof initial segments which satisfy: L0 = ∅, Lλ = ∪α<λLα for limit ordinals λ, and, crucially, Lα + 1 = the collection of 1st order definable subsets of Lα. Since every transitive model of set theory must be closed under 1st order definability, L turns out to be the smallest inner model of set theory. Thus it occupies the central place in the set theoretic spectrum of models.The proof of the continuum hypothesis in L is based on the very uniform hierarchical definition of the L-hierarchy. The Condensation Lemma states that if π : M → Lα is an elementary embedding, M transitive, then some ; the lemma can be proved by induction on α. If a real, i.e., a subset of ω, is definable over some Lα,then by a Löwenheim-Skolem argument it is definable over some countable M as above, and hence over some, < ω1. This allows one to list the reals in L in length ω1 and therefore proves the Continuum Hypothesis in L. (shrink)

We show that if M is a countable transitive model of $\text {ZF}$ and if $a,b$ are reals not in M, then there is a G generic over M such that $b \in L[a,G]$. We then present several applications such as the following: if J is any countable transitive model of $\text {ZFC}$ and $M \not \subseteq J$ is another countable transitive model of $\text {ZFC}$ of the same ordinal height $\alpha $, then there is a forcing extension N of (...) J such that $M \cup N$ is not included in any transitive model of $\text {ZFC}$ of height $\alpha $. Also, assuming $0^{\#}$ exists, letting S be the set of reals generic over L, although S is disjoint from the Turing cone above $0^{\#}$, we have that for any non-constructible real a, $\{ a \oplus s : s \in S \}$ is cofinal in the Turing degrees. (shrink)

We present here an approach to the fine structure of L based solely on elementary model theoretic ideas, and illustrate its use in a proof of Global Square in L. We thereby avoid the Lévy hierarchy of formulas and the subtleties of master codes and projecta, introduced by Jensen [3] in the original form of the theory. Our theory could appropriately be called ”Hyperfine Structure Theory”, as we make use of a hierarchy of structures and hull operations which refines the (...) traditional Lα -or Jα-sequences with their Σn-hull operations.§1. Introduction. In 1938, K. Gödel defined the model L of set theory to show the relative consistency of Cantor's Continuum Hypothesis. L is defined as a unionof initial segments which satisfy: L0 = ∅, Lλ = ∪α<λLα for limit ordinals λ, and, crucially, Lα + 1 = the collection of 1st order definable subsets of Lα. Since every transitive model of set theory must be closed under 1st order definability, L turns out to be the smallest inner model of set theory. Thus it occupies the central place in the set theoretic spectrum of models.The proof of the continuum hypothesis in L is based on the very uniform hierarchical definition of the L-hierarchy. The Condensation Lemma states that if π : M → Lα is an elementary embedding, M transitive, then some ; the lemma can be proved by induction on α. If a real, i.e., a subset of ω, is definable over some Lα,then by a Löwenheim-Skolem argument it is definable over some countable M as above, and hence over some, < ω1. This allows one to list the reals in L in length ω1 and therefore proves the Continuum Hypothesis in L. (shrink)

A classic result of Baumgartner-Harrington-Kleinberg [1] implies that assuming CH a stationary subset of ω1 has a CUB subset in a cardinal-perserving generic extension of V, via a forcing of cardinality ω1. Therefore, assuming that $\omega_2^L$ is countable: { $X \in L \mid X \subseteq \omega_1^L$ and X has a CUB subset in a cardinal -preserving extension of L} is constructible, as it equals the set of constructible subsets of $\omega_1^L$ which in L are stationary. Is there a similar such (...) result for subsets of $\ omega_2^L$ ? Building on work of M. Stanley [9], we show that there is not. We shall also consider a number of related problems, examining the extent to which they are "solvable" in the above sense, as well as defining a notion of reduction between them. (shrink)

We study the Generalized Kurepa hypothesis introduced by Chang. We show that relative to the existence of an inaccessible cardinal the Gap-n-Kurepa hypothesis does not follow from the Gap-m-Kurepa hypothesis for m different from n. The use of an inaccessible is necessary for this result.

An important technique in large cardinal set theory is that of extending an elementary embedding j: M → N between inner models to an elementary embedding j*: M[G] → N[G*] between generic extensions of them. This technique is crucial both in the study of large cardinal preservation and of internal consistency. In easy cases, such as when forcing to make the GCH hold while preserving a measurable cardinal (via a reverse Easton iteration of α-Cohen forcing for successor cardinals α), the (...) generic G* is simply generated by the image of G. But in difficult cases, such as in Woodin's proof that a hypermeasurable is sufficient to obtain a failure of the GCH at a measurable, a preliminary version of G* must be constructed (possibly in a further generic extension of M[G]) and then modified to provide the required G*. In this article we use perfect trees to reduce some difficult cases to easy ones, using fusion as a substitute for distributivity. We apply our technique to provide a new proof of Woodin's theorem as well as the new result that global domination at inaccessibles (the statement that d (κ) is less than 2κ for inaccessible κ, where d (κ) is the dominating number at κ) is internally consistent, given the existence of 0#. (shrink)

In a previous paper with M. Džamonja, class forcings were given which fixed the complexity (a universality covering number) for certain types of structures of size λ together with the value of 2λ for every regular λ. As part of a programme for examining when such global results can be true in an inner model, we build generics for these class forcings.

The continuum function αmaps to2α on regular cardinals is known to have great freedom. Let us say that F is an Easton function iff for regular cardinals α and β, image and α<β→F≤F. The classic example of an Easton function is the continuum function αmaps to2α on regular cardinals. If GCH holds then any Easton function is the continuum function on regular cardinals of some cofinality-preserving extension V[G]; we say that F is realised in V[G]. However if we also wish (...) to preserve measurable cardinals, new restrictions must be put on F. We say that κ is F-hypermeasurable iff there is an elementary embedding j:V→M with critical point κ such that H)Vsubset of or equal toM; j will be called a witnessing embedding. We will show that if GCH holds then for any Easton function F there is a cofinality-preserving generic extension V[G] such that if κ, closed under F, is F-hypermeasurable in V and there is a witnessing embedding j such that j≥F, then κ will remain measurable in V[G]. (shrink)

We show that, assuming the existence of the canonical inner model with one Woodin cardinal $M_1 $, there is a model of $ZFC$ in which the nonstationary ideal on $\omega _1 $ is $\aleph _2 $-saturated and whose reals admit a ${\rm{\Sigma }}_4^1 $-wellorder.

We explore the possibilities for elementary embeddings $j : M \to N$, where M and N are models of ZFC with the same ordinals, $M \subseteq N$, and N has access to large pieces of j. We construct commuting systems of such maps between countable transitive models that are isomorphic to various canonical linear and partial orders, including the real line ${\mathbb R}$.

Let M be a transitive model of ZFC. We say that a transitive model of ZFC, N, is an outer model of M if M ⊆ N and ORD ∩ M = ORD ∩ N. The outer model theory of M is the collection of all formulas with parameters from M which hold in all outer models of M. Satisfaction defined with respect to outer models can be seen as a useful strengthening of first-order logic. Starting from an inaccessible cardinal (...) κ, we show that it is consistent to have a transitive model M of ZFC of size κ in which the outer model theory is lightface definable, and moreover M satisfies V = HOD. The proof combines the infinitary logic L∞,ω, Barwise’s results on admissible sets, and a new forcing iteration of length strictly less than κ+ which manipulates the continuum function on certain regular cardinals below κ. In the Appendix, we review some unpublished results of Mack Stanley which are directly related to our topic. (shrink)

In this article we introduce and study hyperclass-forcing in the context of an extension of Morse-Kelley class theory, called MK∗∗. We define this forcing by using a symmetry between MK∗∗ models and models of ZFC− plus there exists a strongly inaccessible cardinal. We develop a coding between β-models ℳ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$\mathcal {M}$$ \end{document} of MK∗∗ and transitive models M+ of SetMK∗∗ which will allow us to go from ℳ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} (...) \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$\mathcal {M}$$ \end{document} to M+ and vice versa. So instead of forcing with a hyperclass in MK∗∗ we can force over the corresponding SetMK∗∗ model with a class of conditions. For class-forcing to work in the context of ZFC− we show that the SetMK∗∗ model M+ can be forced to look like Lκ∗[X]\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$L_{\kappa ^*}[X]$$ \end{document}, where κ∗ is the height of M+, κ strongly inaccessible in M+ and X ⊆ κ. Over such a model we can apply definable class forcing and we arrive at an extension of M+ from which we can go back to the corresponding β-model of MK∗∗, which will in turn be an extension of the original ℳ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$\mathcal {M}$$ \end{document}. Our main result combines hyperclass forcing with coding methods of Beller et al. and Friedman to show that every β-model of MK∗∗ can be extended to a minimal such model of MK∗∗ with the same ordinals. A simpler version of the proof also provides a new and analogous minimality result for models of second-order arithmetic. (shrink)

The equiconsistency of a measurable cardinal with Mitchell order o=κ++ with a measurable cardinal such that 2κ=κ++ follows from the results by W. Mitchell [13] and M. Gitik [7]. These results were later generalized to measurable cardinals with 2κ larger than κ++ .In Friedman and Honzik [5], we formulated and proved Eastonʼs theorem [4] in a large cardinal setting, using slightly stronger hypotheses than the lower bounds identified by Mitchell and Gitik , for a suitable μ, instead of the cardinals (...) with the appropriate Mitchell order).In this paper, we use a new idea which allows us to carry out the constructions in Friedman and Honzik [5] from the optimal hypotheses. It follows that the lower bounds identified by Mitchell and Gitik are optimal also with regard to the general behavior of the continuum function on regulars in the context of measurable cardinals. (shrink)