We introduce 0• as a sharp for an inner model with a proper class of strong cardinals. We prove the existence of the core model K in the theory “ does not exist”. Combined with work of Woodin, Steel, and earlier work of the author, this provides the last step for determining the exact consistency strength of the assumption in the statement of the 12th Delfino problem pp. 221–224)).

Let 0 < n < ω. If there are n Woodin cardinals and a measurable cardinal above, but $M_{n+1}^{\#}$ doesn't exist, then the core model K exists in a sense made precise. An Iterability Inheritance Hypothesis is isolated which is shown to imply an optimal correctness result for K.

We study the fine structure of the core model for one Woodin cardinal, building of the work of Mitchell and Steel on inner models of the form . We generalize to some combinatorial principles that were shown by Jensen to hold in L. We show that satisfies the statement: “□κ holds whenever κ the least measurable cardinal λ of order λ++”. We introduce a hierarchy of combinatorial principles □κ, λ for 1 λ κ such that □κ□κ, 1 □κ, (...) λ □κ, κ□κ*. We prove that if holds in V. As an application, we show that ZFC + PFA Con. We also obtain one Woodin cardinal as a lower bound on the consistency strength of stationary reflection at κ+ for a singular, countably closed limit cardinal κ such that # exists; likewise for the failure of □κ* at such a κ. (shrink)

We prove that in all Mitchell-Steel core models, □ κ holds for all κ. (See Theorem 2.). From this we obtain new consistency strength lower bounds for the failure of □ κ if κ is either singular and countably closed, weakly compact, or measurable. (Corallaries 5, 8, and 9.) Jensen introduced a large cardinal property that we call subcompactness; it lies between superstrength and supercompactness in the large cardinal hierarchy. We prove that in all Jensen core models, □ (...) κ holds iff κ is not subcompact. (See Theorem 15; the only if direction is essentially due to Jensen.). (shrink)

We prove covering theorems for K, where K is the core model below the sharp for a strong cardinal, and give an application to stationary set reflection.

Let N be a transitive model of ZFC such that ωN ⊂ N and P(R) ⊂ N. Assume that both V and N satisfy "the core model K exists." Then KN is an iterate of K. i.e., there exists an iteration tree J on K such that J has successor length and $\mathit{M}_{\infty}^{\mathit{J}}=K^{N}$. Moreover, if there exists an elementary embedding π: V → N then the iteration map associated to the main branch of J equals π ↾ (...) K. (This answers a question of W. H. Woodin, M. Gitik, and others.) The hypothesis that P(R) ⊂ N is not needed if there does not exist a transitive model of ZFC with infinitely many Woodin cardinals. (shrink)

This paper introduces the real core model K() and determines the extent of scales in this inner model. K() is an analog of Dodd-Jensen's core model K and contains L(), the smallest inner model of ZF containing the reals R. We define iterable real premice and show that Σ1∩() has the scale property when vR AD. We then prove the following Main Theorem: ZF + AD + V = K() DC. Thus, we obtain the (...) Corollary: If ZF + AD +()L() is consistent, then ZF + AD + DC + α < ω2 -AD is also consistent. (shrink)

We survey the definition and fundamental properties of the family of short core models, which extend the core model K of Dodd and Jensen to include α-sequences of measurable cardinals . The theory is applied to various combinatorial principles to get lower bounds for their consistency strengths in terms of the existence of sequences of measurable cardinals. We consider instances of Chang's conjecture, ‘accessible’ Jónsson cardinals, the free subset property for small cardinals, a canonization property of ω (...) ω , and a non-closure property of elementary embeddings of the universe. In some cases, equiconsistencies are obtained. (shrink)

If there is no inner model with a cardinal κ such that o(κ) = κ ++ then the set K ∩ H ω 1 is definable over H ω 1 by a Δ 4 formula, and the set $\{J_\alpha[\mathscr{U}]: \alpha of countable initial segments of the core model K = L[U] is definable over H ω 1 by a Π 3 formula. We show that if there is an inner model with infinitely many measurable cardinals then (...) there is a model in which $\{J_\alpha [\mathscr{U}]: \alpha is not definable by any Σ 3 formula, and K ∩ H ω 1 is not definable by any boolean combination of Σ 3 formulas. (shrink)

We set $\mathscr{D} = \langle\mathscr{D}, \leq_L, \tt\#\rangle$ , where D is the set of degrees of nonconstructibility for countable sets of countable ordinals. We show how to define inductively over this structure the degrees of such sets of ordinals in K, the core model, and the next few core models thereafter, i.e. without reference to mice, premice or measurable cardinals.

We present a general construction of a □κ-sequence in Jensen's fine structural extender models. This construction yields a local definition of a canonical □κ-sequence as well as a characterization of those cardinals κ, for which the principle □κ fails. Such cardinals are called subcompact and can be described in terms of elementary embeddings. Our construction is carried out abstractly, making use only of a few fine structural properties of levels of the model, such as solidity and condensation.

In this paper we shall answer some questions in the set theory of L, the universe of all sets constructible from the reals. In order to do so, we shall assume ADL, the hypothesis that all 2-person games of perfect information on ω whose payoff set is in L are determined. This is by now standard practice. ZFC itself decides few questions in the set theory of L, and for reasons we cannot discuss here, ZFC + ADL yields the most (...) interesting “completion” of the ZFC-theory of L.ADL implies that L satisfies “every wellordered set of reals is countable”, so that the axiom of choice fails in L. Nevertheless, there is a natural inner model of L, namely HODL, which satisfies ZFC.. The superscript “L” indicates, here and below, that the notion in question is to be interpreted in L.) HODL is reasonably close to the full L, in ways we shall make precise in § 1. The most important of the questions we shall answer concern HODL: what is its first order theory, and in particular, does it satisfy GCH?These questions first drew attention in the 70's and early 80's. (shrink)

We study the Magidor iteration of Prikry forcings, and the resulting normal measures on κ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\kappa}$$\end{document}, the first measurable cardinal in a generic extension. We show that when applying the iteration to a core model below 0¶\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${0^{\P}}$$\end{document}, then there exists a natural correspondence between the normal measures on κ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\kappa}$$\end{document} in the ground (...) class='Hi'>model, and those of the generic extension. (shrink)

We follow [8] in asking when a set of ordinals $X \subseteq \alpha$ is a countable union of sets in K, the core model. We show that, analogously to L, and X closed under the canonical Σ 1 Skolem function for K α can be so decomposed provided K is such that no ω-closed filters are put on its measure sequence, but not otherwise. This proviso holds if there is no inner model of a weak Erdős-type property.

We show that if there is no inner model with a Woodin cardinal and the Steel core model K exists, then every Jónsson cardinal is Ramsey in K, and every δ-Jónsson cardinal is δ-Erdös in K. In the absence of the Steel core model K we prove the same conclusion for any model L[E] such that either V = L[E] is the minimal model for a Woodin cardinal, or there is no inner (...) class='Hi'>model with a Woodin cardinal and V is a generic extension of L[E]. The proof includes one lemma of independent interest: If V = L[A], where A $\subset$ κ and κ is regular, then L κ [A] is a Jónsson algebra. The proof of this result, Lemma 2.5, is very short and entirely elementary. (shrink)

Core-periphery imbalances and regional disparities figure prominently on the agenda of several disciplines, which result from their enormous impact on economic and social development around the world. In sociology, international relations, and economics, this concept is crucial in explanations of economic exchange. There are few countries that play a dominant role in world trade, while most countries have a secondary or even a tertiary position in world trade. Moreover, when we are discussing global, continental, regional, and national economies, we (...) can present regions and even smaller territorial units which have higher wages than some underdeveloped areas within the same larger area in focus. Such regional inequalities and injustices are the main themes of the core-periphery model, which focuses on tendencies of economic activities to concentrate around some pivotal points. It seeks to explain the spatial inequalities or imbalances observable on all levels or scales by highlighting the role of horizontal and vertical relations between various entities from the level of towns and cities to the global scale. The existence of a core-periphery structure implies that in the spatial dimension, the socioeconomic development is usually uneven. From such a geographical perspective, the regions known as the "core" are advanced in various areas, while other regions described as the "periphery" serve as a social, economic, and political backstages, backyards, and supply sources or - in some cases - are even subject to degradation and decline. Furthermore, the level of development has a negative correlation with distance from the core. The economies of the states that have gone through various stages of development at the earliest and with the fastest pace have become wealthy core regions and growth poles. Those countries and regions where these processes have been slower become or remain the poor periphery. (shrink)

The grammatical paradigm used to be a model for entire areas of cognitive science. Its primary tenet was that theories are axiomatic-like systems. A secondary tenet was that their predictions should be tested quickly and in great detail with introspective judgments. While the grammatical paradigm now often seems passé, we argue that in fact it continues to be as efficient as ever. Formal models are essential because they are explicit, highly predictive, and typically modular. They make numerous critical predictions, (...) which must be tested efficiently; introspective judgments do just this. We further argue that the grammatical paradigm continues to be fruitful. Within linguistics, implicature theory is a recent example, with a combination of formal explicitness, modularity, and interaction with experimental work. Beyond traditional linguistics, the grammatical paradigm has proven fruitful in the study of gestures and emojis; literature (“Free Indirect Discourse”); picture semantics and comics; music and dance cognition; and even reasoning and concepts. We argue, however, that the grammatical paradigm must be adapted to contemporary cognitive science. Computational methods are essential to derive quantitative predictions from formal models (Bayesian pragmatics is an example). And data collection techniques offer an ever richer continuum of options, from introspective judgments to large-scale experiments, which makes it possible to optimize the cost/benefit ratio of the empirical methods that are chosen to test theories. (shrink)

The multitude of training models and curricula for the specialty of clinical neuropsychology around the world has led to organized activities to develop a framework of core competencies to ensure sufficient expertise among entry-level professionals in the field. The Standing Committee on Clinical Neuropsychology of the European Federation of Psychologists’ Associations is currently working toward developing a specialty certification in clinical neuropsychology to establish a cross-national standard against which to measure levels of equivalency and uniformity in competence and service (...) provision among professionals in the field. Through structured interviews with experts from 28 European countries, we explored potential areas of core competency. Specifically, questions pertained to the perceived importance of a series of foundational, functional, and other competencies, as well as current training standards and practices, and optimal standards. Our findings revealed considerable agreement on academic and clinical training, despite varied actual training requirements currently, with fewer respondents relegating importance to training in teaching, supervision, and research, and even fewer to skills related to management, administration, and advocacy. European expert clinical neuropsychologists were in agreement with previous studies regarding the importance of sound theoretical and clinical training but management, administrative, and advocacy skills were not central to their perspective of a competent specialist in clinical neuropsychology. Establishing a specialty certificate in clinical neuropsychology based on core competencies may enable mobility of clinical neuropsychologists across Europe, and, perhaps, provide an impetus for countries with limited criteria to reconsider their training requirements and harmonize their standards with others. (shrink)

In this paper we prove strong completeness of axiomatic extensions of first-order strict core fuzzy logics with the so-called quasi-witnessed axioms with respect to quasi-witnessed models. As a consequence we obtain strong completeness of Product Predicate Logic with respect to quasi-witnessed models, already proven by M.C. Laskowski and S. Malekpour in [19]. Finally we study similar problems for expansions with Δ, define Δ-quasi-witnessed axioms and prove that any axiomatic extension of a first-order strict core fuzzy logic, expanded with (...) Δ, and Δ-quasi-witnessed axioms are complete with respect to Δ-quasi-witnessed models. (shrink)

Robustness analysis (RA) is the prescription to consider a diverse range of evidence and only regard a hypothesis as well-supported if all the evidence agrees on it. In contexts like climate science, the evidence in support of a hypothesis often comes in the form of model results. This leads to model-based RA (MBRA), whose core notion is that a hypothesis ought to be regarded as well-supported on grounds that a sufficiently diverse set of models agrees on the (...) hypothesis. This chapter, which is the first part of a two-part review of MBRA, begins by providing a detailed statement of the general structure of MBRA. This statement will make visible the various parts of MBRA and will structure the discussion in the remainder of the chapter. The chapter explicates the core concepts of independence and agreement, and it discusses what they mean in the context of climate modeling. The statement shows that MBRA is based on three premises, which concern robust properties, common structures, and so-called robust theorems. The chapter analyzes what these involve and what problems they raise in the context of climate science. In the next chapter, which is the second part of the review, an analysis of how the conclusions of MBRA can be justified is provided. (shrink)

People become addicted in different ways, and they respond differently to different interventions. There may nevertheless be a core neural pathology responsible for all distinctively addictive suboptimal behavioral habits. In particular, timing models of reward learning suggest a hypothesis according to which all addiction involves neuroadaptation that attenuates serotonergic inhibition of a mesolimbic dopamine system that has learned that cues for consumption of the addictive target are signals of a high-reward-rate environment.

Recent decades have witnessed a sea change in thinking about emotion, which has gone from being seen as a disruptive force in human thought and action to being seen as an important source of situation- and goal-relevant information and evaluation, continuous with perception and cognition. Here I argue on philosophical and empirical grounds that the role of emotion in contributing to our ability to respond to reasons for action runs deeper still: The affective system is at the core of (...) the process of evaluatively modeling situations, actions, and outcomes, which is the foundation upon which rational deliberation and action can be built. Taking up this perspective affords new approaches to long-standing problems in the theory of reason-based action. (shrink)

The high pace business environment poses great competition among firms. The key to an organisation’s survival is its workforce. Time taken by the workforce to reach to full proficiency in their job role takes very long in certain job roles. Thus, shortening time-to-proficiency of employees is a critical business problem for today’s organisations. This qualitative research study explored the proven practices and strategies that have successfully reduced time-to-proficiency of the workforce in various settings. A total of 93 participants from seven (...) countries participated in the research study. Bounded project case was used as sampling unit and unit of analysis in this study. This study collected 67 successful project cases with the evidence of significant reduction in time-to-proficiency of the workforce in their settings. These project cases spanned across nine economic sectors, 20 business sectors and 28 industry groups. This study revealed that project leaders across the board used six practices to successfully reduced the time-to-proficiency. The purpose of this paper is present the model of accelerated proficiency at the workplace developed in this study. (shrink)

Esta introdução descreve os mais importantes dados biográficos da vida e da obra do físico teórico austríaco Ludwig Boltzmann (1844-1906). As principais contribuições científicas de Boltzmann situam-se nos domínios da teoria cinética dos gases e mecânica estatística, da qual ele foi um dos fundadores. A tese de que as teorias científicas são representações dos fenômenos naturais é encontrada em todos os artigos de Boltzmann. No verbete "modelo", ela é apresentada de modo mais organizado, o que o torna uma peça fundamental (...) para a compreensão do pensamento filosófico do físico austríaco. O verbete, publicado na famosa enciclopédia Britannica, foi escrito para o público em geral. Ainda assim, Boltzmann não se eximiu de tomar partido em favor do uso de modelos. Estes últimos não apenas seriam inevitáveis, mas necessários, uma vez que tornavam possível o aperfeiçoamento contínuo da ciência. This introduction describes the most important biographical details of the life and work of the Austrian theoretical physicist Ludwig Boltzmann (1844-1906). The main scientific contributions of Boltzmann can be found in areas such as the kinetic theory of gases and statistical mechanics, of which he was one of the co-founders. The thesis that scientific theories are representations of natural phenomena is found in all philosophical articles by Boltzmann. In the entry "model", published in the celebrated Encyclopedia Britannica, the thesis is presented in a more organized way, making it the keystone to understand the philosophical thought of the Austrian physicist. Although the entry was written for the general public, in it Boltzmann did not refrain from taking sides as far as the use of models is concerned. According to him, the latter would not only be inevitable, but in fact necessary, since they would made possible the continuous improvement of science. (shrink)

Guiding core enterprises to participate in supply chain work safety governance is an innovative mode of work safety control, which has an important impact on improving the work safety level of small and medium-sized enterprises in the supply chain. Through in-depth interviews, the grounded theory is adopted to explore the driving factors of work safety management behaviors of core enterprise. It is found that the work safety management behavior of the core enterprise is driven by both internal (...) and external factors. External driving factors are the main category of institutional pressure composed of regulatory pressure, normative pressure, and cognitive pressure. Internal driving factors are divided into the main category of behavioral awareness and the behavioral capability of the core enterprises. The behavioral awareness is composed of responsibility sense, problem cognition and behavioral effect perception. The behavioral capability is composed of safety management strength and safety coordination capability. Institutional pressure, behavioral awareness, and behavioral capability all influence the work safety management behavior of core enterprise in supply chain significantly, but with different ways and paths. On this basis, the driving mechanism model of the above three main categories on the work safety management behavior in core enterprise supply chain is explored. The research can provide targeted policy ideas and implementation paths for the government to formulate effective guiding policies to promote the work safety management behavior of core enterprise. (shrink)

ArgumentThis article uses four historical case studies to address epistemological issues related to the animal model of human diseases and its use in medical research on human diseases. The knowledge derived from animal models is widely assumed to be highly valid and predictive of reactions by human organisms. In this contribution, I use three significant historical cases of failure (ca. 1890, 1960, 2006), and a closer look at the emergence of the concept around 1860/70, to elucidate core assumptions (...) related to the specific practices of animal-human knowledge transfer, and to analyze the explanations provided by historical actors after each of the failures. Based on these examples, I argue that the epistemological status of the animal model changed from that of a helpful methodological tool for addressing specific questions, but with precarious validity, to an obligatory method for the production of strong knowledge on human diseases. As a result, there now exists a culture of biomedical research in human disease that, for more than a century, has taken the value of this methodological tool as self-evident, and more or less beyond question. (shrink)

Research ethics consultation services (RECS), which function as an advisory service to facilitate the resolution of complex ethical issues in clinical research, have been proliferating over the last decade. However, the qualification of an individual who provides RECS, or “a research ethics consultant,” has not been thoroughly investigated, in contrast to healthcare ethics consultants, whose core competencies have been discussed and clarified to a great extent. In this study, we investigated core competencies necessary for research ethics consultants, referring (...) to the core competency models of ethics consultants developed in the healthcare practice context, and propose a competency model for research ethics consultants. (shrink)

This paper delves into the striking parallels between the linguistic patterns of Large Language Models (LLMs) and the concepts of psychosis in Lacanian psychoanalysis. Lacanian theory, with its focus on the formal and logical underpinnings of psychosis, provides a compelling lens to juxtapose human cognition and AI mechanisms. LLMs, such as GPT-4, appear to replicate the intricate metaphorical and metonymical frameworks inherent in human language. Although grounded in mathematical logic and probabilistic analysis, the outputs of LLMs echo the nuanced linguistic (...) associations found in metaphor and metonymy, suggesting a mirroring of human linguistic structures. A pivotal point in this discourse is the exploration of “absolute metaphors”—core gaps in reasoning discernible in both AI models and human thought processes and central to the Lacanian conceptualization of psychosis. Despite the traditional divide between AI research and continental philosophy, this analysis embarks on an innovative journey, utilizing Lacanian philosophy to unravel the logic of AI, using concepts established in the continental discourse on logic, rather than the analytical tradition. (shrink)