We study the filter ℒ*(A) of computably enumerable supersets (modulo finite sets) of an r-maximal set A and show that, for some such set A, the property of being cofinite in ℒ*(A) is still Σ0 3-complete. This implies that for this A, there is no uniformly computably enumerable “tower” of sets exhausting exactly the coinfinite sets in ℒ*(A).

In the vertex pursuit game of cops and robbers on finite graphs, the cop has a winning strategy if and only if the graph admits a dominating order. Such graphs are called constructible in the graph theory literature. This equivalence breaks down for infinite graphs, and variants of the game have been proposed to reestablish partial connections between constructibility and being cop-win. We answer an open question of Lehner about one of these variants by giving examples of weak cop-win graphs (...) which are not constructible. We show that the index set of computable constructible graphs is Π11 hard and the index set of computable constructible locally finite graphs is Π40 hard. Finally, we give an example of a computable constructible graph for which every dominating order computes 0″. (shrink)

We establish that the isomorphism problem for the classes of computable nilpotent rings, distributive lattices, nilpotent groups, and nilpotent semigroups is \-complete, which is as complicated as possible. The method we use is based on uniform effective interpretations of computable binary relations into computable structures from the corresponding algebraic classes.

The aim of this investigation is to explore the role of argumentation schemes in enthymeme reconstruction. This aim is pursued by studying selected cases of incomplete arguments in natural language discourse to see what the requirements are for filling in the unstated premises and conclusions in some systematic and useful way. Some of these cases are best handled using deductive tools, while others respond best to an analysis based on defeasible argumentations schemes. The approach is also shown to work reasonably (...) well for weak arguments, a class of arguments that has always been difficult to analyze without the principle of charity producing a straw man. (shrink)

This work emerged from funded research examining collaboration among stake-holder organizations present at three U.S. nuclear weapons complex sites. The authors examine issues such as how and why stakeholder groups form collaborative alliances when dealing with the target organization, what leaders of stakeholder organizations actually think about when collaborating to deal with the target organization, and what outcomes result from the collaboration process. Drawing on stakeholder theory and research in interorganizational collaboration, the authors used an inductive, interview-based methodology to build (...) a model of collaboration among nonprofit stakeholder groups. The model contributes to the descriptive stream of stakeholder theory and, in turn, has implications for the instrumental stream. The model also offers implications for future researchers, leaders of stakeholder alliances, and leaders of target organizations. (shrink)

We examine the impact of corporate culture on environmental performance using a sample of 7199 firm-year observations over the period of 2002–2018. We find that stronger corporate culture improves environmental performance, measured by the amount of toxic chemical release (TCR). Our result is both statistically and economically significant. We also show that cultural norms of innovation, quality and teamwork as well as a technology-oriented corporate culture have a greater impact on enhancing environmental performance. Further analyses show that managerial competence and (...) strong institutional ownership moderate the relationship between corporate culture and environmental performance. We introduce the decomposition of expected and unexpected components of TCR and document that firms with a strong corporate culture implement strategies to reduce the unexpected component of TCR in addition to the expected component of TCR. Finally, we document that strong corporate culture and environmental performance improve firms’ financial performance. Our results are robust to several sensitivity tests and procedures to mitigate endogeneity and self-selection problems. From a practical point of view, our findings suggest that a firm’s culture can determine its environmental sustainability and ethical practices. (shrink)

We examine the impact of corporate culture on environmental performance using a sample of 7199 firm-year observations over the period of 2002–2018. We find that stronger corporate culture improves environmental performance, measured by the amount of toxic chemical release (TCR). Our result is both statistically and economically significant. We also show that cultural norms of innovation, quality and teamwork as well as a technology-oriented corporate culture have a greater impact on enhancing environmental performance. Further analyses show that managerial competence and (...) strong institutional ownership moderate the relationship between corporate culture and environmental performance. We introduce the decomposition of expected and unexpected components of TCR and document that firms with a strong corporate culture implement strategies to reduce the unexpected component of TCR in addition to the expected component of TCR. Finally, we document that strong corporate culture and environmental performance improve firms’ financial performance. Our results are robust to several sensitivity tests and procedures to mitigate endogeneity and self-selection problems. From a practical point of view, our findings suggest that a firm’s culture can determine its environmental sustainability and ethical practices. (shrink)

Arthur Danto is the Johnsonian Professor Emeritus of Philosophy at Columbia University and the most influential philosopher of art in the last half century. As an art critic for The Nation for 25 years and frequent contributor to other widely read outlets such as the New York Review of Books, Danto also has become one of the most respected public intellectuals of his generation. He is the author of some two dozen important books, along with hundreds of articles and reviews (...) which have been the center of both controversy and discussion. In this volume Danto offers his intellectual autobiography and responds to essays by 27 of the keenest critics of his thought from the worlds of philosophy and the arts. The book includes 16 pages of color art reproductions. Danto is the author dozens of books on art, philosophy, the philosophy of art, and art criticism. He is a rare philosopher who is also a public intellectual. (shrink)

The fundamental question in reverse mathematics is to determine which set existence axioms are required to prove particular theorems of mathematics. In addition to being interesting in their own right, answers to this question have consequences in both effective mathematics and the foundations of mathematics. Before discussing these consequences, we need to be more specific about the motivating question.Reverse mathematics is useful for studying theorems of either countable or essentially countable mathematics. Essentially countable mathematics is a vague term that is (...) best explained by an example. Complete separable metric spaces are essentially countable because, although the spaces may be uncountable, they can be understood in terms of a countable basis. Simpson gives the following list of areas which can be analyzed by reverse mathematics: number theory, geometry, calculus, differential equations, real and complex analysis, combinatorics, countable algebra, separable Banach spaces, computability theory, and the topology of complete separable metric spaces. Reverse mathematics is less suited to theorems of abstract functional analysis, abstract set theory, universal algebra, or general topology.Section 2 introduces the major subsystems of second order arithmetic used in reverse mathematics: RCA0, WKL0, ACA0, ATR0 and – CA0. Sections 3 through 7 consider various theorems of ordered group theory from the perspective of reverse mathematics. Among the results considered are theorems on ordered quotient groups, groups and semigroup conditions which imply orderability, the orderability of free groups, Hölder's Theorem, Mal'tsev's classification of the order types of countable ordered groups. (shrink)

It is known that the spaces of orders on orderable computable fields can represent all Π10 classes up to Turing degree. We show that the spaces of orders on orderable computable abelian and nilpotent groups cannot represent Π10 classes in even a weak manner. Next, we consider presentations of ordered abelian groups, and we show that there is a computable ordered abelian group for which no computable presentation admits a computable set of representatives for its Archimedean classes.

Fossil fuel divestment movements have gained momentum since 2011, aimed at ending fossil fuel use and a move toward a cleaner, affordable, and sustainable energy system, for business and society. The present study investigates the direct impact of fossil fuel divestment announcements on stock prices of firms listed on the United States' stock exchanges. Using an event study and guided by the United Nation's sustainable development goals (SDGs), we test the effects of 116 divestments announcements between 2014 and 2019 on (...) 51 publicly traded fossil fuel companies. Our results suggest that there is a negative effect of these announcements on fossil fuel firm stock prices. Also, we find that the type of fossil fuel firm (coal or oil and gas), the type of divestment (partial, coal only, or full), the timing of the announcement, and the size of the divesting investor have some explanatory power in relation to the (cumulative) abnormal returns following the divestment announcements. While the negative impact on stock prices is not surprising, the reaction from the divested firms after such large divestitures is not consistent with what may be expected, given past reactions to divestitures seeking to achieve different social goals. Given the SDGs, it seems clear why investors are divesting themselves from fossil fuel firms, but why has the reaction to the 116 divestments led to very little change in the way these publicly traded fossil fuel firms do business given their direct and growing impacts on society? We conclude the study with some suggestions for future research. (shrink)

This volume frames the question of responsibility as a problem of agency in relation to the systems and structures of globalization. According to Ricoeur responsibility is a “shattered concept” when considered too narrowly as a problem of act, agency and individual freedom. To examine this Esther Reed develops a short genealogy of modern liberal and post-liberal concepts of responsibility in order to understand better the relationship dominant modern framings of the meanings of responsibility. Reed engages with writings by (...) major modern (Schleiermacher, Hegel, Marx, Weber) and post-liberal (Buber, Levinas, Derrida, Badiou, Butler, Young, Critchley) theorists to illustrate the shift from an ethnic responsibility built on notions of accountability and attributions to an ethic responsibility that starts variously from the 'other'. Reed sees Dietrich Bonhoeffer as the most promising partner of this theological dialogue, as his learning of responsibility from the risen Christ present now in the (global) church is a welcome provocation to new thinking about the meaning of responsibility learned from land, distant neighbour, (global) church and the bible. Bonhoeffer's reflections on the centre, boundaries and limits of responsibility remain helpful to Christian people struggling with an increasingly exhausted concept of accountability. (shrink)

We study theorems of ordered groups from the perspective of reverse mathematics. We show that suffices to prove Hölder's Theorem and give equivalences of both (the orderability of torsion free nilpotent groups and direct products, the classical semigroup conditions for orderability) and (the existence of induced partial orders in quotient groups, the existence of the center, and the existence of the strong divisible closure).

In recent years, there has been a substantial amount of work in reverse mathematics concerning natural mathematical principles that are provable from RT, Ramsey's Theorem for Pairs. These principles tend to fall outside of the "big five" systems of reverse mathematics and a complicated picture of subsystems below RT has emerged. In this paper, we answer two open questions concerning these subsystems, specifically that ADS is not equivalent to CAC and that EM is not equivalent to RT.

We examine the Dual Ramsey Theorem and two related combinatorial principles VW(k,l) and OVW(k,l) from the perspectives of reverse mathematics and effective mathematics. We give a statement of the Dual Ramsey Theorem for open colorings in second order arithmetic and formalize work of Carlson and Simpson [1] to show that this statement implies ACA 0 over RCA 0 . We show that neither VW(2,2) nor OVW(2,2) is provable in WKL 0 . These results give partial answers to questions posed by (...) Friedman and Simpson [3]. (shrink)

We show that every countable ideal of degrees that are low for isomorphism is contained in a principal ideal of degrees that are low for isomorphism by adapting an exact pair construction. We further show that within the hyperimmune free degrees, lowness for isomorphism is entirely independent of computable traceability.

This volume reaches beyond the controversy surrounding the teaching and learning of evolution in the United States, specifically in regard to the culture, politics, and beliefs found in the Southeast. The editors argue that despite a deep history of conflict in the region surrounding evolution, there is a wealth of evolution research taking place—from biodiversity in species to cultural evolution and human development. In fact, scientists, educators, and researchers from around the United States have found their niche in the South, (...) where biodiversity is high, culture runs deep, and the pace is just a little bit slower. (shrink)

This special report is published in commemoration of the fiftieth anniversary of the “Report of the Ad Hoc Committee of the Harvard Medical School to Examine the Definition of Brain Death,” a landmark document that proposed a new way to define death, with implications that advanced the field of organ transplantation. This remarkable success notwithstanding, the concept has raised lasting questions about what it means to be dead. Is death defined in terms of the biological failure of the organism to (...) maintain integrated functioning? Can death be declared on the basis of severe neurological injury even when biological functions remain intact? Is death essentially a social construct that can be defined in different ways, based on human judgment? These issues, and more, are discussed and debated in this report by leading experts in the field, many of whom have been engaged with this topic for decades. (shrink)

We analyze three applications of Ramsey’s Theorem for 4-tuples to infinite traceable graphs and finitely generated infinite lattices using the tools of reverse mathematics. The applications in graph theory are shown to be equivalent to Ramsey’s Theorem while the application in lattice theory is shown to be provable in the weaker system RCA0.

We study the implications of model completeness of a theory for the effectiveness of presentations of models of that theory. It is immediate that for a computable model A\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal {A}$$\end{document} of a computably enumerable, model complete theory, the entire elementary diagram E\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$E$$\end{document} must be decidable. We prove that indeed a c.e. theory T is model complete if and only if there is a (...) uniform procedure that succeeds in deciding E\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$E$$\end{document} from the atomic diagram Δ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varDelta $$\end{document} for all countable models A\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal {A}$$\end{document} of T. Moreover, if every presentation of a single isomorphism type A\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal {A}$$\end{document} has this property of relative decidability, then there must be a procedure with succeeds uniformly for all presentations of an expansion \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$$$\end{document} by finitely many new constants. (shrink)

The terms of the upper and lower central series of a nilpotent computable group have computably enumerable Turing degree. We show that the Turing degrees of these terms are independent even when restricted to groups which admit computable orders.

This special volume of Studies in Christian Ethics constitutes the most significant continuation to date of Christian social ethics in the tradition of Ronald Preston. It brings together leading scholars and new voices in the field from around the world, covering a broad range of contemporary issues, including globalisation, poverty, feminism, civil society, economics and religious pluralism.

We characterize the structure of computably categorical trees of finite height, and prove that our criterion is both necessary and sufficient. Intuitively, the characterization is easiest to express in terms of isomorphisms of (possibly infinite) trees, but in fact it is equivalent to a Σ03-condition. We show that all trees which are not computably categorical have computable dimension ω. Finally, we prove that for every n≥ 1 in ω, there exists a computable tree of finite height which is δ0n+1-categorical but (...) not δ0n-categorical. (shrink)

Early versions of satellite and radiosonde datasets suggested that the tropical surface had warmed more than the troposphere, while climate models consistently showed tropospheric amplification of surface warming in response to human-caused increases in greenhouse gases. We revisit such comparisons here using new observational estimates of surface and tropospheric temperature changes. We find that there is no longer a serious discrepancy between modeled and observed trends in the tropics. Our results contradict a recent claim that all simulated temperature trends in (...) the tropical troposphere are inconsistent with observations. This claim was based on the use of older radiosonde and satellite datasets and on two methodological errors: the neglect of observational trend uncertainties introduced by interannual climate variability and application of an inappropriate statistical “consistency test”.This emerging reconciliation of models and observations has two primary explanations. First, because of changes in the treatment of buoy and satellite information, new surface temperature datasets yield slightly reduced tropical warming relative to earlier versions. Second, recently developed satellite and radiosonde datasets now show larger warming of the tropical lower troposphere. In the case of a new satellite dataset from remote sensing systems, enhancedRSS warming is due to an improved procedure of adjusting for inter-satellite biases. When the RSS-derived tropospheric temperature trend is compared with four different observed estimates of surface temperature change, the surface warming is invariably amplified in the tropical troposphere, consistent with model results. Even if we use data from a second satellite dataset with smaller tropospheric warming than in remote sensing systems RSS, observed tropical lapse rates are not significantly different from those in all model simulations.Our results contradict a recent claim that all simulated temperature trends in the tropical troposphere and in tropical lapse rates are inconsistent with observations. This claim was based on the use of older radiosonde and satellite datasets and on two methodological errors: the neglect of observational trend uncertainties introduced by interannual climate variability and application of an inappropriate statistical “consistency test”. (shrink)