Before one can construct scales of minimal complexity in the Real Core Model, K(R), one needs to develop the fine-structure theory of K(R). In this paper, the fine structure theory of mice, first introduced by Dodd and Jensen, is generalized to that of real mice. A relative criterion for mouse iterability is presented together with two theorems concerning the definability of this criterion. The proof of the first theorem requires only fine structure; whereas, the second theorem applies to real mice (...) satisfying AD and follows from a general definability result obtained by abstracting work of John Steel on L(R). In conclusion, we discuss several consequences of the work presented in this paper relevant to two issues: the complexity of scales in K(R) and the strength of the theory ZF + AD + ¬ DC R. (shrink)

BackgroundNo standard method exists to assess how many consults a healthcare ethics consultation (HCEC) service should perform. To address this, we developed a method to estimate the volume of HCEC services based on a mixed-methods approach that included a systematic review and survey data on the volume of consult services requested.MethodsOur investigation included a systematic review of studies that reported the volume of HCEC services that were requested from 2000 to 2017, institutional surveys, and statistical analyses that estimated the volume (...) of HCEC services that were adjusted to the size of the hospitals in the survey and to population acuity.ResultsWe contacted the authors of 19 studies that met our inclusion criteria; 17 authors responded to the institutional survey and five provided annualized data points. We found that standard methods of reporting the volume of HCEC services led to inaccuracies in estimating the growth of HCEC services over time. To rectify this, we proposed two means to estimate volume based on either the service goals of HCEC services or hospital size and acuity.DiscussionThe statistical limitations of our study highlight the need to standardize the sharing and reporting of data in clinical ethics. Future work should further standardize methods of HCEC quality assessment using measures similar to those we describe. (shrink)

Current accounts suggest that self-referential thought serves a pivotal function in the human ability to simulate the future during mind-wandering. Using experience sampling, this hypothesis was tested in two studies that explored the extent to which self-reflection impacts both retrospection and prospection during mind-wandering. Study 1 demonstrated that a brief period of self-reflection yielded a prospective bias during mind-wandering such that participants’ engaged more frequently in spontaneous future than past thought. In Study 2, individual differences in the strength of self-referential (...) thought — as indexed by the memorial advantage for self rather than other-encoded items — was shown to vary with future thinking during mind-wandering. Together these results confirm that self-reflection is a core component of future thinking during mind-wandering and provide novel evidence that a key function of the autobiographical memory system may be to mentally simulate events in the future. (shrink)

Propositional logic -- Predicate logic -- Proof strategies and diagrams -- Mathematical induction -- Set theory -- Functions -- Relations -- Core concepts in abstract algebra -- Core concepts in real analysis.

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 show, using the fine structure of K, that the theory ZF + AD + X R[X K] implies the existence of an inner model of ZF + AD + DC containing a measurable cardinal above its Θ, the supremum of the ordinals which are the surjective image of R. As a corollary, we show that HODK = K for some P K where K is the Dodd-Jensen Core Model relative to P. In conclusion, we show that the theory ZF (...) + AD + ¬DCR implies that R† exists. (shrink)

For over three decades, clinical ethicists in the United States have recorded their consulting activities to supplement documentation in the medical record, often using locally developed instrument...

Jensen's celebrated Covering Lemma states that if 0# does not exist, then for any uncountable set of ordinals X, there is a Y∈L such that X⊆Y and |X| = |Y|. Working in ZF + AD alone, we establish the following analog: If ℝ# does not exist, then L(ℝ) and V have exactly the same sets of reals and for any set of ordinals X with |X| ≥ΘL(ℝ), there is a Y∈L(ℝ) such that X⊆Y and |X| = |Y|. Here ℝ is (...) the set of reals and Θ is the supremum of the ordinals which are the surjective image of ℝ. (shrink)

Working in ZF+AD alone, we prove that every set of ordinals with cardinality at least Θ can be covered by a set of ordinals in HOD of K (ℝ) of the same cardinality, when there is no inner model with an ℝ-complete measurable cardinal. Here ℝ is the set of reals and Θ is the supremum of the ordinals which are the surjective image of ℝ.

After showing that \ refutes \ for all regular cardinals \, we present a diamond-plus principle \ concerning all subsets of \. Using a forcing argument, we prove that \ holds in Steel’s core model \}}\), an inner model in which the axiom of determinacy can hold. The combinatorial principle \ is then extended, in \}}\), to successor cardinals \ and to certain cardinals \ that are not ineffable. Here \ is the supremum of the ordinals that are the surjective (...) image of the set of reals \. (shrink)

Mathematical Logic: An Introduction is a textbook that uses mathematical tools to investigate mathematics itself. In particular, the concepts of proof and truth are examined. The book presents the fundamental topics in mathematical logic and presents clear and complete proofs throughout the text. Such proofs are used to develop the language of propositional logic and the language of first-order logic, including the notion of a formal deduction. The text also covers Tarski’s definition of truth and the computability concept. It also (...) provides coherent proofs of Godel’s completeness and incompleteness theorems. Moreover, the text was written with the student in mind and thus, it provides an accessible introduction to mathematical logic. In particular, the text explicitly shows the reader how to prove the basic theorems and presents detailed proofs throughout the book. Most undergraduate books on mathematical logic are written for a reader who is well-versed in logical notation and mathematical proof. This textbook is written to attract a wider audience, including students who are not yet experts in the art of mathematical proof. (shrink)

Given that \(L(\mathbb {R})\models {\text {ZF}}+ {\text {AD}}+{\text {DC}}\), we present conditions under which one can generically add new elements to \(L(\mathbb {R})\) and obtain a model of \({\text {ZF}}+ {\text {AD}}+{\text {DC}}\). This work is motivated by the desire to identify the smallest cardinal \(\kappa \) in \(L(\mathbb {R})\) for which one can generically add a new subset \(g\subseteq \kappa \) to \(L(\mathbb {R})\) such that \(L(\mathbb {R})(g)\models {\text {ZF}}+ {\text {AD}}+{\text {DC}}\).

We prove within K\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${K}$$\end{document} that the axiom of determinacy is equivalent to the assertion that for each ordinal λ λ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\kappa > \lambda}$$\end{document}. Here Θ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\Theta}$$\end{document} is the supremum of the ordinals which are the surjective image of the set of reals R\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb{R}}$$\end{document}.

Three studies were conducted to explore the psychological determinants of COVID-deterrent behaviors. In Study 1, using data collected and analyzed both before and after the release of COVID-19 vaccines, mask-wearing, other preventative behaviors like social distancing, and vaccination intentions were positively related to assessments of the Coronavirus Behavioral Health Mindset ; belief in the credibility of science; progressive political orientation; less use of repressive and more use of sensitization coping; and the attribution of COVID-19 safety to effort rather than ability, (...) powerful forces, fate, or luck. In Study 2, favorable COVID-19 vaccination intentions were related to greater willingness to work, lower emotional distress, and greater customer experience mindset. Study 3 examined the personality and motives of individuals who volunteered to help deliver COVID-19 inoculations to the local community. The vaccine-giving volunteers, especially those with prosocial motives, had high CVBHM scores, belief in the credibility of science, low use of repressive coping, greater attribution of COVID-19 protection to effort, low likelihood of voting conservative, were older, and had more education than others. The majority of public health volunteers expressed prosocial motives to help people or join a cause, but many expressed the personal motives of getting the COVID-19 vaccination for themselves, conveying a public image of compassion, or structuring time. Based on the three research studies, a COVID-19 Mindset Hierarchy model is proposed to integrate the results. (shrink)

Analogous to prism adaptation, sensorimotor compensation for existing neural delays has been clearly demonstrated. This system can also adapt to new delays, both internal and external. This seems to occur at least partially in the sensor systems, and works for discrete, stationary events. This provides additional evidence for visual prediction, but not in a manner that is consistent with spatial extrapolation.

The Dodd–Jensen Covering Lemma states that “if there is no inner model with a measurable cardinal, then for any uncountable set of ordinals X, there is a \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${Y\in K}$$\end{document} such that \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${X\subseteq Y}$$\end{document} and |X| = |Y|”. Assuming ZF+AD alone, we establish the following analog: If there is no inner model with an \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb (...) {R}}$$\end{document} –complete measurable cardinal, then the real core model \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${K(\mathbb {R})}$$\end{document} is a “very good approximation” to the universe of sets V; that is, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${K(\mathbb {R})}$$\end{document} and V have exactly the same sets of reals and for any set of ordinals X with \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${|{X}|\ge\Theta}$$\end{document}, there is a \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${Y\in K(\mathbb {R})}$$\end{document} such that \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${X\subseteq Y}$$\end{document} and |X| = |Y|. Here \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb {R}}$$\end{document} is the set of reals and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\Theta}$$\end{document} is the supremum of the ordinals which are the surjective image of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb {R}}$$\end{document}. (shrink)

We estimate that 208,000 deep brain stimulation (DBS) devices have been implanted to address neurological and neuropsychiatric disorders worldwide. DBS Think Tank presenters pooled data and determined that DBS expanded in its scope and has been applied to multiple brain disorders in an effort to modulate neural circuitry. The DBS Think Tank was founded in 2012 providing a space where clinicians, engineers, researchers from industry and academia discuss current and emerging DBS technologies and logistical and ethical issues facing the field. (...) The emphasis is on cutting edge research and collaboration aimed to advance the DBS field. The Eighth Annual DBS Think Tank was held virtually on September 1 and 2, 2020 (Zoom Video Communications) due to restrictions related to the COVID-19 pandemic. The meeting focused on advances in: (1) optogenetics as a tool for comprehending neurobiology of diseases and on optogenetically-inspired DBS, (2) cutting edge of emerging DBS technologies, (3) ethical issues affecting DBS research and access to care, (4) neuromodulatory approaches for depression, (5) advancing novel hardware, software and imaging methodologies, (6) use of neurophysiological signals in adaptive neurostimulation, and (7) use of more advanced technologies to improve DBS clinical outcomes. There were 178 attendees who participated in a DBS Think Tank survey, which revealed the expansion of DBS into several indications such as obesity, post-traumatic stress disorder, addiction and Alzheimer’s disease. This proceedings summarizes the advances discussed at the Eighth Annual DBS Think Tank. (shrink)

Using a Levy hierarchy and a fine structure theory for \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${K(\mathbb{R})}$$\end{document}, we obtain scales of minimal complexity in this inner model. Each such scale is obtained assuming the determinacy of only those sets of reals whose complexity is strictly below that of the scale constructed.

The world of John Dewey scholarship recently lost one of its most thoughtful contributors, and teachers of all kinds lost one of their most passionate and committed advocates. Philip W. Jackson was born in 1928 in Vineland, New Jersey, a locale known historically for its excellent grape-growing soil and veterinarian Arthur Goldhaft’s famous pledge to “put a chicken in every pot.” Jackson’s adoptive parents were, appropriately enough, chicken farmers, and, as the story goes, they noticed early on his indisputable knack (...) for singing and poetry recitation. Feeling very at home on the stage, the plucky six-year-old even tried his hand as a vaudevillian, performing a snake charmer act between reels at.. (shrink)

We typically think of prosecutorial ethics as encompassing a special set of obligations for prosecutors during the pretrial and trial stages of a criminal case. In the literature and in rules of professional responsibility much attention is paid to the charging function, contact with unrepresented persons, plea negotiations, discovery, and courtroom decorum. Our concern with prosecutorial ethics at these stages is rooted primarily in due process and fairness to the accused. [W]hile he may strike hard blows, the Supreme Court wrote (...) in Berger v. United States, [a prosecutor] is not at liberty to strike foul ones. Whether it is a recognition that the prosecutor acts as a representative of the sovereign or that he or she possesses extraordinary power over people's lives, we speak about the prosecutor's ethical duties as special or additional to those of ordinary lawyers. By preventing a prosecutor from litigating unfairly, the aim is to protect a criminal defendant from an unjust or unwarranted conviction. What, then, are the ethical duties of prosecutors after the defendant has had his fair shot at trial, but lost? The literature and standards are surprisingly silent, with rare exception, on the post-conviction ethics of prosecutors. Constraints on the prosecutorial function seem to reach their apex at trial. Why? Are the reasons for special or additional ethics for prosecutors non-existent on appeal? Is the vast discretion, present at the pretrial and trial stages and thought by some to justify special ethical duties, absent on appeal? As a recent case from Texas illustrates, ethical issues still abound even after a jury returns a verdict of guilty. Nevertheless, the traditional discourse on pre-conviction duties can help us determine how prosecutorial discretion should be exercised after a conviction has been obtained. (shrink)

López-Escobar, E. G. K. Introduction.--Kueker, D. W. Back-and-forth arguments and infinitary logics.--Green, J. Consistency properties for finite quantifier languages.--Cunningham, E. Chain models.--Gregory, J. On a finiteness condition for infinitary languages.

In lieu of an abstract, here is a brief excerpt of the content:Keeping Philosophy in Mind:Shadworth H. Hodgson's Articulation of the Boundaries of Philosophy and ScienceThomas W. StaleyIntroductionShadworth H. Hodgson's (1832–1912) contributions to Victorian intellectual discourse have faded from prominence over the past century. However, despite his current anonymity, Hodgson's case is important to an understanding of the historical split between philosophy and science in late nineteenth century Britain. In particular, his example illuminates the specific role played by developing concepts (...) of the mind in a period of deep transition in the British intellectual community. His virtual disappearance from the record, I contend, is indicative also of the disappearance of his form of philosophy as a vital social project. His ideas, rather than being rejected, were instead largely neglected—they became lost as philosophical discussion moved elsewhere, both conceptually and institutionally. However, in the inaugural volume of Mind in 1876, Hodgson's ideas initially found a prominent place in a central dialogue over the position of philosophy with respect to science. There, and throughout his career, Hodgson engaged in the defense of an intellectual tradition he regarded as under threat from psychological science. Both his particular formulation of an ongoing role for philosophy and his own uneasy position in the intellectual environment of late Victorian Britain shed significant light on an under-examined issue [End Page 289] of the period: the fraught relationship between philosophy and science as competing enterprises engaged in the study of the human mind."Philosophy" and "science" are easily construed as partnered intellectual complexes in modern Western society. However, closer scrutiny of the historical record shows that the two terms—whether as theoretical referents or actors' categories—have often reflected divergent priorities and that transitions from "philosophical" to "scientific" terms have been contentious. In examining the birth of natural science out of natural philosophy during the Enlightenment, the historian Andrew Cunningham has emphasized how the reordering of intellectual fields created new conflictive relationships between philosophy, science, and religion.1 He reminds us that the process of scientific secularization was but one of a set of constitutive shifts among these human activities, and that the earlier natural philosophy thus played by fundamentally different rules than its successor. A similar story can be told about the late nineteenth-century transition I am considering: in a nutshell, to borrow a phrase from Cunningham, men did not start doing mental science until they stopped doing moral philosophy. However, this time, philosophy already stood in competition with existing scientific institutions, sparking a more severe contest for authority. As mental science began to develop along the lines of the natural disciplines, Hodgson and others feared little would remain as a distinctive domain for philosophy as such, moral or otherwise. His efforts on the part of philosophy thus represent one front in an intellectual "turf war"—what recent scholars have called "boundary work," shoring up the institutional positions of different intellectual enterprises competing for authority in the world.2 Gieryn's formative analysis of boundary work was based on the contemporaneous example of John Tyndall's campaign to promote scientific over religious authority in Victorian Britain, but this was much more than a two-way struggle. The early career of Mind bears witness to a closely related, but less discussed, battle for influence between philosophy and science, in which the journal itself served as a critical "boundary object," a medium for enforcement of the distinctions between these two intellectual fields.3 [End Page 290]Thomas Dixon has recently surveyed the origins of this shift. Like Cunningham, Dixon emphasizes the constitutive differences in scope and orientation of the two intellectual enterprises, salient among them the secularization of the new human sciences.4 This process—begun tentatively by Thomas Brown and brought to fruition by Bain, Spencer, and Darwin—involved wholesale shifts in the scholarly linguistic complex, from a set of several mental categories rooted in Christian philosophical categories—affections, passions, sentiments, etc.—to a novel, explicitly "scientific," and singular grouping of emotions. While the older tradition dominant until mid-century had understood the broad range of mental phenomena as largely rational and voluntary, the new emotions were formulated as more circumscribed in purview, subconscious or autonomic in action... (shrink)

"A very fine piece of work, essential reading for anyone concerned with Kant, Aristotelian ethics, practical reason, and more generally, the foundations of moral value and justification.... The examples are a real strength, insightful and very well-chosen."--Anthony Cunningham, St. John's University "The issues Harris has taken on are among the most important in contemporary moral thinking, and he has handled them systematically, innovatively, wisely, with wit and good sense."--J. K. Swindler, Wittenberg University.

Given the cultural dominance of the empirical sciences, it is perhaps inevitable that theology should seek a self-understanding that emulates them. Yet post-modern thinkers concur in rejecting Enlightenment canons of knowledge as too restrictive for any discipline seeking to fathom our own humanity, a pursuit that theology shares with literature. In both fields, language, as an engagement with symbols, is not the pursuit of an object of knowledge so much as an act ofself expression and an opening to communion. This (...) is illustrated by an examination of the life and work of Virginia Woolf, as she is revivified in Michael Cunningham’s novel, The Hours. Its explication is drawn from the writing of the German Jesuit theologian Karl Rahner, who insisted that St. Thomas Aquinas viewed all of reality as essentially self expressive, and the human person as that spot in creation, ordered toward all that is and achieving self-constitutionthrough symbolic intercourse with others. (shrink)