Since 1997, FORUM has been an integral part of the landscape of European studies. In addition to contemporary history, it offers insights into the history of ideas and reviews books on Central and Eastern European history. It offers more than just history--for instance, interdisciplinary discussions by political scientists, literary, legal, and economic scholars, and philosophers. FORUM sees itself as a bridge between East and West. Through the translation and publication of texts and contributions from Russian, Polish, and Czech researchers, it (...) offers the Western reader access to the scholarly discourse of Eastern Europe. The 'short' 20th century is one of the best-documented eras in history. Nevertheless, it holds more mysteries than many periods of antiquity or the Middle Ages of which we have only sparse relics. One of the biggest mysteries is the question of the causes of the collapse of civilization in the first half of the century. In Germany as well as in Russia, regimes came to power invoking the implementation of utopias that had been dreamt up during the 'long' 19th century yet which had been considered unrealizable. Now, it turned out, even the most radical utopian blueprint could be put into place. This development, intertwined with an extraordinarily deep crisis of European democracy, did not happen overnight. It had been looming for a long time. There had even been several prescient voices heralding the upcoming crisis--trailing away without being noticed. Volume 19, Issue 1 of FORUM recognizes some of these unheard prophets and scrutinizes their writings. (shrink)

We prove that there are groups in the constructible universe whose automorphism towers are highly malleable by forcing. This is a consequence of the fact that, under a suitable diamond hypothesis, there are sufficiently many highly rigid non-isomorphic Souslin trees whose isomorphism relation can be precisely controlled by forcing.

We introduce three families of diagonal reflection principles for matrices of stationary sets of ordinals. We analyze both their relationships among themselves and their relationships with other known principles of simultaneous stationary reflection, the strong reflection principle, and the existence of square sequences.

It is shown that the Magidor forcing to collapse the cofinality of a measurable cardinal that carries a length \ sequence of normal ultrafilters, increasing in the Mitchell order, to \, is subcomplete.

The effects of the forcing axioms \, \ and \ on the failure of weak threaded square principles of the form \\) are analyzed. To this end, a diagonal reflection principle, \, and it implies the failure of \\) if \. It is also shown that this result is sharp. It is noted that \/\ imply the failure of \\), for every regular \, and that this result is sharp as well.

For an arbitrary forcing class Γ, the Γ-fragment of Todorčević’s strong reflection principle SRPis isolated in such a way that the forcing axiom for Γ implies the Γ-fragment of SRP, the sta...

For an ordinal \, I introduce a variant of the notion of subcompleteness of a forcing poset, which I call \-subcompleteness, and show that this class of forcings enjoys some closure properties that the original class of subcomplete forcings does not seem to have: factors of \-subcomplete forcings are \-subcomplete, and if \ and \ are forcing-equivalent notions, then \ is \-subcomplete iff \ is. I formulate a Two Step Theorem for \-subcompleteness and prove an RCS iteration theorem for \-subcompleteness (...) which is slightly less restrictive than the original one, in that its formulation is more careful about the amount of collapsing necessary. Finally, I show that an adequate degree of \-subcompleteness follows from the \-distributivity of a forcing, for \. (shrink)

The main result of this paper is the following theorem: Let M be a premouse with a top extender, F. Suppose that (a) M is linearly coarsely iterable via hitting F and its images, and (b) if M * is a linear iterate of M as in (a), then M * is coarsely iterable with respect to iteration trees which do not use the top extender of M * and its images. Then M is coarsely iterable.

Ehrenfeucht’s lemma asserts that whenever one element of a model of Peano arithmetic is definable from another, they satisfy different types. We consider here the analogue of Ehrenfeucht’s lemma for models of set theory. The original argument applies directly to the ordinal-definable elements of any model of set theory, and, in particular, Ehrenfeucht’s lemma holds fully for models of set theory satisfying V=HOD. We show that the lemma fails in the forcing extension of the universe by adding a Cohen real. (...) We go on to formulate a scheme of natural parametric generalizations of Ehrenfeucht’s lemma, namely, the principles of the form EL, which asserts that P-definability from A implies Q-discernibility. We also consider various analogues of Ehrenfeucht’s lemma obtained by using algebraicity in place of definability, where a set b is algebraic in a if it is a member of a finite set definable from a. Ehrenfeucht’s lemma holds for the ordinal-algebraic sets, we prove, if and only if the ordinal-algebraic and ordinal-definable sets coincide. Using a similar analysis, we answer two open questions posed earlier by the third author and C. Leahy, showing that algebraicity and definability need not coincide in models of set theory and the internal and external notions of being ordinal algebraic need not coincide. (shrink)

I analyze the hierarchies of the bounded and the weak bounded forcing axioms, with a focus on their versions for the class of subcomplete forcings, in terms of implications and consistency strengths. For the weak hierarchy, I provide level-by-level equiconsistencies with an appropriate hierarchy of partially remarkable cardinals. I also show that the subcomplete forcing axiom implies Larson’s ordinal reflection principle atω2, and that its effect on the failure of weak squares is very similar to that of Martin’s Maximum.

I develop a translation procedure between λ-structures, which correspond to premice in the Friedman–Jensen indexing convention on the one hand and s-structures, which are essentially the same as premice in the Mitchell–Steel indexing scheme.

l investigate versions of the Maximality Principles for the classes of forcings which are <κ-closed. <κ-directed-closed, or of the form Col (κ. <Λ). These principles come in many variants, depending on the parameters which are allowed. I shall write MPΓ(A) for the maximality principle for forcings in Γ, with parameters from A. The main results of this paper are: • The principles have many consequences, such as <κ-closed-generic $\Sigma _{2}^{1}(H_{\kappa})$ absoluteness, and imply. e.g., that ◇κ holds. I give an application (...) to the automorphism tower problem, showing that there are Souslin trees which are able to realize any equivalence relation, and hence that there are groups whose automorphism tower is highly sensitive to forcing. • The principles can be separated into a hierarchy which is strict, for many κ. • Some of the principles can be combined, in the sense that they can hold at many different κ simultaneously. The possibilities of combining the principles are limited, though: While it is consistent that MP<κ-closed(HκT) holds at all regular κ below any fixed α. the "global" maximality principle, stating that MP<κ-closed(Hκ ∪ {κ}) holds at every regular κ. is inconsistent. In contrast to this, it is equiconsistent with ZFC that the maximality principle for directed-closed forcings without any parameters holds at every regular cardinal. It is also consistent that every local statement with parameters from HκT that's provably <κ-closed-forceably necessary is true, for all regular κ. (shrink)

We investigate various strong notions of rigidity for Souslin trees, separating them under ♢ into a hierarchy. Applying our methods to the automorphism tower problem in group theory, we show under ♢ that there is a group whose automorphism tower is highly malleable by forcing.

A generalization of Příkrý's forcing is analyzed which adjoins to a model of ZFC a set of order type at most ω below each member of a discrete set of measurable cardinals. A characterization of generalized Příkrý generic sequences reminiscent of Mathias' criterion for Příkrý genericity is provided, together with a maximality theorem which states that a generalized Příkrý sequence almost contains every other one lying in the same extension.This forcing can be used to falsify the covering lemma for a (...) higher core model if there is an inner model with infinitely many measurable cardinals – changing neither cardinalities nor cofinalities. Another application is an alternative proof of a theorem of Mitchell stating that if the core model contains a regular limit θ of measurable cardinals, then there is a model in which every set of measurable cardinals of K bounded in θ has an indiscernible sequence but there is no such sequence for the entire set of measurables of K below θ. (shrink)

I investigate the relationships between three hierarchies of reflection principles for a forcing class $\Gamma $ : the hierarchy of bounded forcing axioms, of $\Sigma ^1_1$ -absoluteness, and of Aronszajn tree preservation principles. The latter principle at level $\kappa $ says that whenever T is a tree of height $\omega _1$ and width $\kappa $ that does not have a branch of order type $\omega _1$, and whenever ${\mathord {\mathbb P}}$ is a forcing notion in $\Gamma $, then it is (...) not the case that ${\mathord {\mathbb P}}$ forces that T has such a branch. $\Sigma ^1_1$ -absoluteness serves as an intermediary between these principles and the bounded forcing axioms. A special case of the main result is that for forcing classes that don’t add reals, the three principles at level $2^\omega $ are equivalent. Special attention is paid to certain subclasses of subcomplete forcing, since these are natural forcing classes that don’t add reals. (shrink)

The motivation for this paper is the following: In [4] I showed that it is inconsistent with ZFC that the Maximality Principle for directed closed forcings holds at unboundedly many regular cardinals κ (even only allowing κ itself as a parameter in the Maximality Principle for < κ -closed forcings each time). So the question is whether it is consistent to have this principle at unboundedly many regular cardinals or at every regular cardinal below some large cardinal κ (instead of (...) ∞), and if so. how strong it is. It turns out that it is consistent in many cases, but the consistency strength is quite high. (shrink)

We examine the moderating role of the situational and organizational contexts in determining unethical managerial behavior, applying the case-survey methodology. On the basis of a holistic, multiple-antecedent perspective, we hypothesize that two key constructs, moral intensity and situational strength, help explain contextual moderating effects on relationships between managers’ individual characteristics and unethical behavior. Based on a quantitative analysis of 52 case studies describing occurrences of real-life unethical conduct, we find empirical support for the hypothesized contextual moderating effects of moral intensity (...) and situational strength. By examining these complex contextual moderators, we aim to contribute to organizational ethics research as we shed light on the critical role that context may play in influencing unethical managerial behavior. (shrink)

Continuing the work of Fuchs [1], I show that the translation functions developed previously map iterable λ-structures to iterable s-structures and vice versa. To this end, I analyse how the translation functions interact with the formation of extender ultrapowers and normal iterations. This analysis makes it possible to translate iterations, and, in a last step, iteration strategies, thus arriving at the result.

I analyze the hierarchies of the bounded resurrection axioms and their “virtual” versions, the virtual bounded resurrection axioms, for several classes of forcings. I analyze these axioms in terms of implications and consistency strengths. For the virtual hierarchies, I provide level-by-level equiconsistencies with an appropriate hierarchy of virtual partially super-extendible cardinals. I show that the boldface resurrection axioms for subcomplete or countably closed forcing imply the failure of Todorčević’s square at the appropriate level. I also establish connections between these hierarchies (...) and the hierarchies of bounded and weak bounded forcing axioms. (shrink)

It is shown that the boldface maximality principle for subcomplete forcing,, together with the assumption that the universe has only set many grounds, implies the existence of a well‐ordering of definable without parameters. The same conclusion follows from, assuming there is no inner model with an inaccessible limit of measurable cardinals. Similarly, the bounded subcomplete forcing axiom, together with the assumption that does not exist, for some, implies the existence of a well‐ordering of which is Δ1‐definable without parameters, and ‐definable (...) using a subset of ω1 as a parameter. This well‐order is in. Enhanced versions of bounded forcing axioms are introduced that are strong enough to have the implications of mentioned above, and along the way, a bounded forcing axiom for countably closed forcing is proposed. (shrink)

I prove that there is a recursive function T that does the following: Let X be transitive and rudimentarily closed, and let X ′ be the closure of X ∪ {X } under rudimentary functions. Given a Σ0-formula φ and a code c for a rudimentary function f, T is a Σω-formula such that for any equation image ∈ X, X ′ ⊧ φ [f ] iff X ⊧ T [equation image]. I make this precise and show relativized versions of (...) this. As an application, I prove that under certain conditions, if Y is the Σω extender ultrapower of X with respect to some extender F that also is an extender on X ′, then the closure of Y ∪ {Y } under rudimentary functions is the Σ0 extender ultrapower of X′ with respect to F, and the ultrapower embeddings agree on X. (shrink)

A highly rigid Souslin tree T is constructed such that forcing with T turns T into a Kurepa tree. Club versions of previously known degrees of rigidity are introduced, as follows: for a rigidity property P, a tree T is said to have property P on clubs if for every club set C (containing 0), the restriction of T to levels in C has property P. The relationships between these rigidity properties for Souslin trees are investigated, and some open questions (...) are stated. (shrink)

In this note, I will list instances where in the literature on subcomplete forcing and its forcing principles (mostly in articles of my own), the assumption of the continuum hypothesis, or that we are working above the continuum, was omitted. I state the correct statements and provide or point to correct proofs. There are also some new results, most of which revolve around showing the necessity of the extra assumption.

I use generic embeddings induced by generic normal measures on that can be forced to exist if κ is an indestructibly weakly compact cardinal. These embeddings can be applied in order to obtain the forcing axioms in forcing extensions. This has consequences in : The Singular Cardinal Hypothesis holds above κ, and κ has a useful Jónsson-like property. This in turn implies that the countable tower works much like it does when κ is a Woodin limit of Woodin cardinals. One (...) consequence is that every set of reals in the Chang model is Lebesgue measurable and has the Baire Property, the Perfect Set Property and the Ramsey Property. So indestructible weak compactness has effects on cardinal arithmetic high up and also on the structure of sets of real numbers, down low, similar to supercompactness. (shrink)

We extend the results of Hamkins and Thomas concerning the malleability of automorphism tower heights of groups by forcing. We show that any reasonable sequence of ordinals can be realized as the automorphism tower heights of a certain group in consecutive forcing extensions or ground models, as desired. For example, it is possible to increase the height of the automorphism tower by passing to a forcing extension, then increase it further by passing to a ground model, and then decrease it (...) by passing to a further forcing extension, and so on, transfinitely. We make sense of the limit models occurring in such a sequence of models. At limit stages, the automorphism tower height will always be 1. (shrink)

We show that the analogues of the embedding theorems of [3], proved for the countable models of set theory, do not hold when extended to the uncountable realm of ω1‐like models of set theory. Specifically, under the ⋄ hypothesis and suitable consistency assumptions, we show that there is a family of many ω1‐like models of, all with the same ordinals, that are pairwise incomparable under embeddability; there can be a transitive ω1‐like model of that does not embed into its own (...) constructible universe; and there can be an ω1‐like model of whose structure of hereditarily finite sets is not universal for the ω1‐like models of set theory. (shrink)

I analyze various natural assumptions which imply that the set {ω1L[x]∣x⊆ω}\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\{\omega_1^{L[x]} \mid x \subseteq \omega\}}$$\end{document} is stationary in ω1. The focal questions are which implications hold between them, what their consistency strengths are, and which large cardinal assumptions outright imply them.

We introduce and consider the inner-model reflection principle, which asserts that whenever a statement \varphi(a) in the first-order language of set theory is true in the set-theoretic universe V, then it is also true in a proper inner model W \subset A. A stronger principle, the ground-model reflection principle, asserts that any such \varphi(a) true in V is also true in some non-trivial ground model of the universe with respect to set forcing. These principles each express a form of width (...) reflection in contrast to the usual height reflection of the Lévy–Montague reflection theorem. They are each equiconsistent with ZFC and indeed \Pi_2-conservative over ZFC, being forceable by class forcing while preserving any desired rank-initial segment of the universe. Furthermore, the inner-model reflection principle is a consequence of the existence of sufficient large cardinals, and lightface formulations of the reflection principles follow from the maximality principle MP and from the inner-model hypothesis IMH. We also consider some questions concerning the expressibility of the principles. (shrink)

A diagonal version of the strong reflection principle is introduced, along with fragments of this principle associated with arbitrary forcing classes. The relationships between the resulting principles and related principles, such as the corresponding forcing axioms and the corresponding fragments of the strong reflection principle, are analyzed, and consequences are presented. Some of these consequences are “exact” versions of diagonal stationary reflection principles of sets of ordinals. We also separate some of these diagonal strong reflection principles from related axioms.

We explore Woodin's Universality Theorem and consider to what extent large cardinal properties are transferred into HOD (and other inner models). We also separate the concepts of supercompactness, supercompactness in HOD and being HOD-supercompact. For example, we produce a model where a proper class of supercompact cardinals are not HOD-supercompact but are supercompact in HOD. Additionally we introduce a way to measure the degree of HOD-supercompactness of a supercompact cardinal, and we develop methods to control these degrees simultaneously for a (...) proper class of supercompact cardinals. Finally, we also produce a model in which the unique supercompact cardinal is also the only strongly compact cardinal, no cardinal is supercompact up to an inaccessible cardinal, level by level inequivalence holds and the unique supercompact cardinal is not HOD-supercompact. (shrink)

Problems and choices -- Who shall live? -- The physician : the captain of the team -- The hospital : the house of hope -- Drugs : the key to modern medicine -- Paying for medical care.

The relationship between education and democratic development has been a growing theme in debates focussed upon public education, but there has been little work that has directly related educational leadership to wider issues of freedom, politics and practice. Engaging with ELMA through the work of Hannah Arendt enables these issues of power to be directly confronted. Arendt produced texts that challenged notions of freedom and politics, and notably examined the lives of people, ideas and historical events in ways that are (...) pertinent to the purposes and practices of education. This significant volume examines the main texts in the Arendt library and explains each of the key ideas and how they can enable critical thinking about knowledge production and practice in educational leadership. The analysis draws upon a range of exemplars and empirical projects from the field of educational leadership, investigating utility issues regarding Arendt's ideas, and engaging with the debates concerning her insights and contribution. Included in the book: -using Arendt to think about ELMA -the relationship between policy and practice, and organisation and leadership -critiques of the Vita Activa and Vita Contemplativa -thinking with and against Arendt. Gunter uses the work of Arendt to challenge the purposes and practices of intellectual work, with a view to developing perspectives on the responsibility for research and ideas. The book will be of value to all those working and researching in the field of Educational Leadership, Management and Administration. (shrink)

Figal has long been recognized as one of the most insightful interpreters working in the tradition of philosophical hermeneutics and its leading themes concerned with ancient Greek thought, art, language, and history. With this book, Figal presses this tradition of philosophical hermeneutics in new directions. In his effort to forge philosophical hermeneutics into a hermeneutical philosophy, Figal develops an original critique of the objectification of the world that emerges in modernity as the first stage in his systematic treatment of the (...) elements of experience hermeneutically understood. Breaking through the prejudices of modernity, but not sacrificing the importance and challenge of the objective world that confronts us and is in need of interpretation, Figal reorients how it is that philosophy should take up some of its most longstanding and stubborn questions. World, object, space, language, freedom, time, and life are refreshed as philosophical notions here since they are each regarded as elements of human life engaged in the task assigned to each of us—the task of understanding ourselves and our world. (shrink)

Since the beginning of business research and teaching, the basic assumptions of the discipline have been intensely debated. One of these basic assumptions concerns the behavioral aspects of human beings, which are traditionally represented in the construct of homo economicus. These assumptions have been increasingly challenged in light of findings from social, ethnological, psychological, and ethical research. Some publications from an integrative perspective have suggested that homo economicus embodies to a high degree dark character traits, particularly related to the construct (...) of psychopathy, representing individuals who are extremely self-centered and ruthless, without feelings of remorse or compassion. While a growing body of research notes such a similarity on a more or less anecdotal basis, this article aims to explore this connection from a more rigorous perspective, bridging insights from psychological, economic, and business research to better understand the potentially dark traits of homo economicus. The analysis shows that homo economicus is not simply some kind of psychopath, but specifically a so-called subclinical or Factor 1 psychopath, who is also referred to as a “corporate psychopath” in business research. With such an analysis, the paper adds an additional perspective and a deeper psychological level of understanding as to why homo economicus is often controversially debated. Based on these insights, several implications for academic research and teaching are discussed and reflected upon in light of an ethics of virtue and care. (shrink)