Capitalism is the best. It's free enterprise. Barter. Gimbels, if I get really rank with the clerk, 'Well I don't like this', how I can resolve it? If it really gets ridiculous, I go, 'Frig it, man, I walk.' What can this guy do at Gimbels, even if he was the president of Gimbels? He can always reject me from that store, but I can always go to Macy's. He can't really hurt me. Communism is like one big phone company. (...) Government control, man. And if I get too rank with that phone company, where can I go? I'll end up like a schmuck with a dixie cup on a thread. (shrink)

In thinking and talking about rights, including property rights, it seems natural to put the argument in either moral or legal terms. From the former viewpoint, rights are part of a description of what actions are right or wrong. The fact that I have a right to do something is an argument, although not necessarily a sufficient argument, that someone who prevents me from doing it is acting wrongly.

1. A NOTE ON INTERPRETATION It became clear in the discussions at the conference at which Professor Brody's paper was given that he and I had slightly different interpretations of his paper. He apparently regards the rights violations to be justified as events in the distant past, and any resulting compensation as being due to our contemporaries only as heirs of people injured in the distant past. To me, one of the attractions of his analysis is that it allows one (...) to dispense with such tenuous arguments and consider rights violations occuring at this very moment, and the compensation due for them. If every individual has the right to use all uncreated resources, then when I use force to keep you out of my living room I am violating your rights; although that may be an appropriate rights violation, it still imposes on me the obligation to compensate you. These comments were originally written on the assumption that Professor Brody intended the argument to be interpreted in this way; since I believe it is a more interesting argument in that form than in the form apparently intended by its author, I will maintain that interpretation throughout my comments. 2. CRITIQUE Professor Brody's solution to the problem of Lockean entitlements is ingenious and in some ways attractive, but I find it unsatisfactory in the form presented here. The problem is that, in spite of the author's claims to the contrary, it seems impossible, in principle, to decide how much compensation each person is entitled to. (shrink)

The definition above nicely encapsulates two of the intertwined meanings of ‘privacy’. In the first sense— physical seclusion —the level of privacy in modern developed societies is extraordinarily high by historical standards. We take it for granted that a bed in a hotel will be occupied by either one person or a couple—not by several strangers. At home, few of us expect to share either bed or bedroom with our children. In these and a variety of other ways, increased physical (...) privacy has come as a byproduct of increased wealth. (shrink)

Israel has a long history of concern with chemical and biological threats, since several hostile states in the Middle East are likely to possess such weapons. The Twin-Tower terrorist attacks and Anthrax envelope scares of 2001 were a watershed for public perceptions of the threat of unconventional terror in general and of biological terror in particular. New advances in biotechnology will only increase the ability of terrorists to exploit the burgeoning availability of related information to develop ever-more destructive bioweapons. Many (...) areas of modern biological research are unavoidably dual-use by nature. They thus have a great potential for both help and harm; and facilitating the former while preventing the latter remains a serious challenge to researchers and governments alike. This article addresses how Israel might best (1) prevent hostile elements from obtaining, from Israel’s biological research system, materials, information and technologies that might facilitate their carrying out a biological attack, while (2) continuing to promote academic openness, excellence and other hallmarks of that system. This important and sensitive issue was assessed by a special national committee, and their recommendations are presented and discussed. One particularly innovative element is the restructuring and use of Israel’s extensive biosafety system to also address biosecurity goals, with minimal disruption or delay. (shrink)

End-of-life care is the only major reference to systematically explore the unique medical, social, legal, political, and ethical issues to consider while providing care to adults and children with intellectual and developmental disabilities who are facing terminal illness or life-limiting conditions.

By forcing over a model of with a class-sized partial order preserving this theory we produce a model in which there is a locally defined well-order of the universe; that is, one whose restriction to all levels H is a well-order of H definable over the structure H, by a parameter-free formula. Further, this forcing construction preserves all supercompact cardinals as well as all instances of regular local supercompactness. It is also possible to define variants of this construction which, in (...) addition to forcing a locally defined well-order of the universe, preserve many of the n-huge cardinals from the ground model. (shrink)

Assuming ${2^{{N_0}}}$ = N₁ and ${2^{{N_1}}}$ = N₂, we build a partial order that forces the existence of a well-order of H(ω₂) lightface definable over ⟨H(ω₂), Є⟩ and that preserves cardinal exponentiation and cofinalities.

In this article, we first offer a model of design knowledge types and their interrelationships in value sensitive design. Then we demonstrate that value sensitive design is a formative framework, which provides a shaping influence on practice, enables creative appropriation, and supports theory and method development.

Using the Friedman-Koepke Hyperfine Structure Theory of [2], we provide a short construction of a gap 1 morass in the constructible universe.

This paper addresses the knowledge required for individuals to evaluate Information and Communications Technologies decisions that relate to the organization and management of cyberspace, and to hold accountable the parties responsible for those decisions, whether the responsible party is a government actor, market actor or private individual. The authors argue that the Open Systems Interconnection model, with certain modifications, should serve as a primary educational tool in helping individuals to gain the understanding of ICT necessary to protect public interests related (...) to cyberspace. (shrink)

A central area of current philosophical debate in the foundations of mathematics concerns whether or not there is a single, maximal, universe of set theory. Universists maintain that there is such a universe, while Multiversists argue that there are many universes, no one of which is ontologically privileged. Often model-theoretic constructions that add sets to models are cited as evidence in favour of the latter. This paper informs this debate by developing a way for a Universist to interpret talk that (...) seems to necessitate the addition of sets to V. We argue that, despite the prima facie incoherence of such talk for the Universist, she nonetheless has reason to try and provide interpretation of this discourse. We present a method of interpreting extension-talk (V-logic), and show how it captures satisfaction in `ideal' outer models and relates to impredicative class theories. We provide some reasons to regard the technique as philosophically virtuous, and argue that it opens new doors to philosophical and mathematical discussions for the Universist. (shrink)

We review different conceptions of the set-theoretic multiverse and evaluate their features and strengths. In Sect. 1, we set the stage by briefly discussing the opposition between the ‘universe view’ and the ‘multiverse view’. Furthermore, we propose to classify multiverse conceptions in terms of their adherence to some form of mathematical realism. In Sect. 2, we use this classification to review four major conceptions. Finally, in Sect. 3, we focus on the distinction between actualism and potentialism with regard to the (...) universe of sets, then we discuss the Zermelian view, featuring a ‘vertical’ multiverse, and give special attention to this multiverse conception in light of the hyperuniverse programme introduced in Arrigoni and Friedman (2013). We argue that the distinctive feature of the multiverse conception chosen for the hyperuniverse programme is its utility for finding new candidates for axioms of set theory. (shrink)

The Hyperuniverse Program is a new approach to set-theoretic truth which is based on justifiable principles and leads to the resolution of many questions independent from ZFC. The purpose of this paper is to present this program, to illustrate its mathematical content and implications, and to discuss its philosophical assumptions.

We study the complexity of the isomorphism relation on classes of computable structures. We use the notion of FF-reducibility introduced in [9] to show completeness of the isomorphism relation on many familiar classes in the context of all ${\mathrm{\Sigma }}_{1}^{1}$ equivalence relations on hyperarithmetical subsets of ω.

We review different conceptions of the set-theoretic multiverse and evaluate their features and strengths. In Sect. 1, we set the stage by briefly discussing the opposition between the ‘universe view’ and the ‘multiverse view’. Furthermore, we propose to classify multiverse conceptions in terms of their adherence to some form of mathematical realism. In Sect. 2, we use this classification to review four major conceptions. Finally, in Sect. 3, we focus on the distinction between actualism and potentialism with regard to the (...) universe of sets, then we discuss the Zermelian view, featuring a ‘vertical’ multiverse, and give special attention to this multiverse conception in light of the hyperuniverse programme introduced in Arrigoni-Friedman :77–96, 2013). We argue that the distinctive feature of the multiverse conception chosen for the hyperuniverse programme is its utility for finding new candidates for axioms of set theory. (shrink)

There are two standard ways to establish consistency in set theory. One is to prove consistency using inner models, in the way that Gödel proved the consistency of GCH using the inner model L. The other is to prove consistency using outer models, in the way that Cohen proved the consistency of the negation of CH by enlarging L to a forcing extension L[G].But we can demand more from the outer model method, and we illustrate this by examining Easton's strengthening (...) of Cohen's result:Theorem 1. There is a forcing extensionL[G] of L in which GCH fails at every regular cardinal.Assume that the universe V of all sets is rich in the sense that it contains inner models with large cardinals. Then what is the relationship between Easton's model L[G] and V? In particular, are these models compatible, in the sense that they are inner models of a common third model? If not, then the failure of GCH at every regular cardinal is consistent only in a weak sense, as it can only hold in universes which are incompatible with the universe of all sets. Ideally, we would like L[G] to not only be compatible with V, but to be an inner model of V.We say that a statement is internally consistent iff it holds in some inner model, under the assumption that there are innermodels with large cardinals. (shrink)

Relative to a hyperstrong cardinal, it is consistent that measure one covering fails relative to HOD. In fact it is consistent that there is a superstrong cardinal and for every regular cardinal κ, κ + is greater than κ + of HOD. The proof uses a very general lemma showing that homogeneity is preserved through certain reverse Easton iterations.

Using countable support iterations of S-proper posets, we show that the existence of a definable wellorder of the reals is consistent with each of the following: , and.

There have been numerous results showing that a measurable cardinal κ can carry exactly α normal measures in a model of GCH, where a is a cardinal at most κ⁺⁺. Starting with just one measurable cardinal, we have [9] (for α = 1), [10] (for α = κ⁺⁺, the maximum possible) and [1] (for α = κ⁺, after collapsing κ⁺⁺) . In addition, under stronger large cardinal hypotheses, one can handle the remaining cases: [12] (starting with a measurable cardinal of (...) Mitchell order α ) , [2] (as in [12], but where κ is the least measurable cardinal and α is less than κ, starting with a measurable of high Mitchell order) and [11] (as in [12], but where κ is the least measurable cardinal, starting with an assumption weaker than a measurable cardinal of Mitchell order 2). In this article we treat all cases by a uniform argument, starting with only one measurable cardinal and applying a cofinality-preserving forcing. The proof uses κ-Sacks forcing and the "tuning fork" technique of [8]. In addition, we explore the possibilities for the number of normal measures on a cardinal at which the GCH fails. (shrink)

The study of Borel equivalence relations under Borel reducibility has developed into an important area of descriptive set theory. The dichotomies of Silver [20] and Harrington, Kechris and Louveau [6] show that with respect to Borel reducibility, any Borel equivalence relation strictly above equality on ω is above equality on , the power set of ω, and any Borel equivalence relation strictly above equality on the reals is above equality modulo finite on . In this article we examine the effective (...) content of these and related results by studying effectively Borel equivalence relations under effectively Borel reducibility. The resulting structure is complex, even for equivalence relations with finitely many equivalence classes. However use of Kleene’s O as a parameter is sufficient to restore the picture from the noneffective setting. A key lemma is that of the existence of two effectively Borel sets of reals, neither of which contains the range of the other under any effectively Borel function; the proof of this result applies Barwise compactness to a deep theorem of Harrington establishing for any recursive ordinal α the existence of singletons whose α-jumps are Turing incomparable. (shrink)

I discuss three potential sources of evidence for truth in set theory, coming from set theory’s roles as a branch of mathematics and as a foundation for mathematics as well as from the intrinsic maximality feature of the set concept. I predict that new non first-order axioms will be discovered for which there is evidence of all three types, and that these axioms will have significant first-order consequences which will be regarded as true statements of set theory. The bulk of (...) the paper is concerned with the Hyperuniverse Programme, whose aim is to discover an optimal mathematical principle for expressing the maximality of the set-theoretic universe in height and width. (shrink)

In this article, we report on eight grand challenges for value sensitive design, which were developed at a one-week workshop, Value Sensitive Design: Charting the Next Decade, Lorentz Center, Leiden, The Netherlands, November 14–18, 2016. A grand challenge is a substantial problem, opportunity, or question that motives sustained research and design activity. The eight grand challenges are: Accounting for Power, Evaluating Value Sensitive Design, Framing and Prioritizing Values, Professional and Industry Appropriation, Tech policy, Values and Human Emotions, Value Sensitive Design (...) and Intelligent Algorithms, and Value Tensions. Each grand challenge consists of a discussion of its importance and a set of tractable key questions. (shrink)

In this paper we are concerned about the ways GCH can fail in relation to rank-into-rank hypotheses, i.e., very large cardinals usually denoted by I3, I2, I1 and I0. The main results are a satisfactory analysis of the way the power function can vary on regular cardinals in the presence of rank-into-rank hypotheses and the consistency under I0 of the existence of j:Vλ+1≺Vλ+1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${j : V_{\lambda+1} {\prec} V_{\lambda+1}}$$\end{document} with the failure of GCH (...) at λ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\lambda}$$\end{document}. (shrink)

The fact that “natural” theories, i.e. theories which have something like an “idea” to them, are almost always linearly ordered with regard to logical strength has been called one of the great mysteries of the foundation of mathematics. However, one easily establishes the existence of theories with incomparable logical strengths using self-reference . As a result, PA+Con is not the least theory whose strength is greater than that of PA. But still we can ask: is there a sense in which (...) PA+Con is the least “natural” theory whose strength is greater than that of PA? In this paper we exhibit natural theories in strength strictly between PA and PA+Con by introducing a notion of slow consistency. (shrink)

We show that there is a [Formula: see text]-model of second-order arithmetic in which the choice scheme holds, but the dependent choice scheme fails for a [Formula: see text]-assertion, confirming a conjecture of Stephen Simpson. We obtain as a corollary that the Reflection Principle, stating that every formula reflects to a transitive set, can fail in models of [Formula: see text]. This work is a rediscovery by the first two authors of a result obtained by the third author in [V. (...) G. Kanovei, On descriptive forms of the countable axiom of choice, Investigations on nonclassical logics and set theory, Work Collect., Moscow, 3-136 ]. (shrink)

We show that is consistent with the existence of a -definable wellorder of the reals and a -definable ω-mad subfamily of [ω]ω.

We study the structure of Σ11 equivalence relations on hyperarithmetical subsets of ω under reducibilities given by hyperarithmetical or computable functions, called h-reducibility and FF-reducibility, respectively. We show that the structure is rich even when one fixes the number of properly equation imagei.e., Σ11 but not equation image equivalence classes. We also show the existence of incomparable Σ11 equivalence relations that are complete as subsets of ω × ω with respect to the corresponding reducibility on sets. We study complete Σ11 (...) equivalence relations and show that existence of infinitely many properly Σ11 equivalence classes that are complete as Σ11 sets is necessary but not sufficient for a relation to be complete in the context of Σ11 equivalence relations. (shrink)

Discussion of new axioms for set theory has often focused on conceptions of maximality, and how these might relate to the iterative conception of set. This paper provides critical appraisal of how certain maximality axioms behave on different conceptions of ontology concerning the iterative conception. In particular, we argue that forms of multiversism (the view that any universe of a certain kind can be extended) and actualism (the view that there are universes that cannot be extended in particular ways) face (...) complementary problems. The latter view is unable to use maximality axioms that make use of extensions, where the former has to contend with the existence of extensions violating maximality axioms. An analysis of two kinds of multiversism, a Zermelian form and Skolemite form, leads to the conclusion that the kind of maximality captured by an axiom differs substantially according to background ontology. (shrink)

In this paper we introduce some fusion properties of forcing notions which guarantee that an iteration with supports of size ⩽κ not only does not collapse κ+ but also preserves the strength of κ. This provides a general theory covering the known cases of tree iterations which preserve large cardinals [3], Friedman and Halilović [5], Friedman and Honzik [6], Friedman and Magidor [8], Friedman and Zdomskyy [10], Honzik [12]).

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

In this paper we review the most common forms of reflection and introduce a new form which we call sharp-generated reflection. We argue that sharp-generated reflection is the strongest form of reflection which can be regarded as a natural generalization of the Lévy reflection theorem. As an application we formulate the principle sharp-maximality with the corresponding hypothesis IMH#. IMH# is an analogue of the IMH :591–600, 2006)) which is compatible with the existence of large cardinals.

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

In this paper we review the most common forms of reflection and introduce a new form which we call sharp‐generated reflection. We argue that sharp‐generated reflection is the strongest form of reflection which can be regarded as a natural generalization of the Lévy reflection theorem. As an application we formulate the principle sharp‐maximality with the corresponding hypothesis. The statement is an analogue of the (Inner Model Hypothesis, introduced in ) which is compatible with the existence of large cardinals.