Chapter 1: Introduction. S = <{We}c<w; C,U,n,0,w> is the substructure formed by restricting the lattice <^P(w); C , U, n,0,w> to the re subsets We of the ...

We explore the interaction between Lebesgue measure and dominating functions. We show, via both a priority construction and a forcing construction, that there is a function of incomplete degree that dominates almost all degrees. This answers a question of Dobrinen and Simpson, who showed that such functions are related to the proof-theoretic strength of the regularity of Lebesgue measure for Gδ sets. Our constructions essentially settle the reverse mathematical classification of this principle.

We study the proof-theoretic strength and effective content of the infinite form of Ramsey's theorem for pairs. Let RT n k denote Ramsey's theorem for k-colorings of n-element sets, and let RT $^n_{ denote (∀ k)RT n k . Our main result on computability is: For any n ≥ 2 and any computable (recursive) k-coloring of the n-element sets of natural numbers, there is an infinite homogeneous set X with X'' ≤ T 0 (n) . Let IΣ n and BΣ (...) n denote the Σ n induction and bounding schemes, respectively. Adapting the case n = 2 of the above result (where X is low 2 ) to models of arithmetic enables us to show that RCA 0 + IΣ 2 + RT 2 2 is conservative over RCA 0 + IΣ 2 for Π 1 1 statements and that $RCA_0 + I\Sigma_3 + RT^2_{ , is Π 1 1 -conservative over RCA 0 + IΣ 3 . It follows that RCA 0 + RT 2 2 does not imply BΣ 3 . In contrast, J. Hirst showed that $RCA_0 + RT^2_{ does imply BΣ 3 , and we include a proof of a slightly strengthened version of this result. It follows that $RT^2_{ is strictly stronger than RT 2 2 over RCA 0. (shrink)

The goal of this paper is to announce there is a single orbit of the c.e. sets with inclusion, ε, such that the question of membership in this orbit is ${\Sigma _1^1 }$ -complete. This result and proof have a number of nice corollaries: the Scott rank of ε is $\omega _1^{{\rm{CK}}}$ + 1; not all orbits are elementarily definable; there is no arithmetic description of all orbits of ε; for all finite α ≥ 9, there is a properly $\Delta (...) _\alpha ^0 $ orbit (from the proof). (shrink)

We show there is a non-recursive r.e. set A such that if W is any low r.e. set, then the join W $\oplus$ A is also low. That is, A is "almost deep". This answers a question of Jockusch. The almost deep degrees form an definable ideal in the r.e. degrees (with jump.).

We show that the double jump is definable in the computably enumerable sets. Our main result is as follows: let [Formula: see text] is the Turing degree of a [Formula: see text] set J ≥T0″}. Let [Formula: see text] such that [Formula: see text] is upward closed in [Formula: see text]. Then there is an ℒ property [Formula: see text] such that [Formula: see text] if and only if there is an A where A ≡T F and [Formula: see text]. (...) A corollary of this is that, for all n ≥ 2, the high n computably enumerable degrees are invariant in the computably enumerable sets. Our work resolves Martin's Invariance Conjecture. (shrink)

The main result of this paper is to show that for every recursive ordinal α ≠ 0 and for every nonrecursive r.e. degree d there is a r.e. set of rank α and degree d.

We state and prove the Translation Theorem. Then we apply the Translation Theorem to Soare's Extension Theorem, weakening slightly the hypothesis to yield a theorem we call the Modified Extension Theorem. We use this theorem to reprove several of the known results about orbits in the lattice of recursively enumerable sets. It is hoped that these proofs are easier to understand than the old proofs.

In this article we establish the existence of a number of new orbits in the automorphism group of the computably enumerable sets. The degree theoretical aspects of these orbits also are examined.

The purpose of this communication is to announce some recent results on the computably enumerable sets. There are two disjoint sets of results; the first involves invariant classes and the second involves automorphisms of the computably enumerable sets. What these results have in common is that the guts of the proofs of these theorems uses a new form of definable coding for the computably enumerable sets.We will work in the structure of the computably enumerable sets. The language is just inclusion, (...) ⊆. This structure is called ε.All sets will be computably enumerable non-computable sets and all degrees will be computably enumerable and non-computable, unless otherwise noted. Our notation and definitions are standard and follow Soare [1987]; however we will warm up with some definitions and notation issues so the reader need not consult Soare [1987]. Some historical remarks follow in Section 2.1 and throughout Section 3.We will also consider the quotient structure ε modulo the ideal of finite sets, ε*. ε* is a definable quotient structure of ε since “Χ is finite” is definable in ε; “Χ is finite” iff all subsets of Χ are computable. We use A* to denote the equivalent class of A under the ideal of finite sets. (shrink)

Let b and c be r.e. Turing degrees such that b>c. We show that there is an r.e. degree a such that b>a>c and all lattices containing a critical triple, including the lattice M5, cannot be embedded into the interval [c, a].

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.

A result of Soare and Stob asserts that for any non-recursive r.e. setC, there exists a r.e.[C] setA such thatA⊕C is not of r.e. degree. A setY is called [of]m-REA (m-REA[C] [degree] iff it is [Turing equivalent to] the result of applyingm-many iterated ‘hops’ to the empty set (toC), where a hop is any function of the formX→X ⊕W e X . The cited result is the special casem=0,n=1 of our Theorem. Form=0,1, and any (m+1)-REA setC, ifC is not ofm-REA (...) degree, then for alln there exists an-r.e.[C] setA such thatA ⊕C is not of (m+n)-REA degree. We conjecture that this holds also form≥2. (shrink)

Soare [20] proved that the maximal sets form an orbit in${\cal E}$. We consider here${\cal D}$-maximal sets, generalizations of maximal sets introduced by Herrmann and Kummer [12]. Some orbits of${\cal D}$-maximal sets are well understood, e.g., hemimaximal sets [8], but many are not. The goal of this paper is to define new invariants on computably enumerable sets and to use them to give a complete nontrivial classification of the${\cal D}$-maximal sets. Although these invariants help us to better understand the${\cal D}$-maximal (...) sets, we use them to show that several classes of${\cal D}$-maximal sets break into infinitely many orbits. (shrink)

We show that if A and $\widehat{A}$ are automorphic via Φ then the structures $S_{R}(A)$ and $S_{R}(\widehat{A})$ are $\Delta_{3}^{0}-isomorphic$ via an isomorphism Ψ induced by Φ. Then we use this result to classify completely the orbits of hhsimple sets.

A computably enumerable (c.e.) degree is a maximal contiguous degree if it is contiguous and no c.e. degree strictly above it is contiguous. We show that there are infinitely many maximal contiguous degrees. Since the contiguous degrees are definable, the class of maximal contiguous degrees provides the first example of a definable infinite anti-chain in the c.e. degrees. In addition, we show that the class of maximal contiguous degrees forms an automorphism base for the c.e. degrees and therefore for the (...) Turing degrees in general. Finally we note that the construction of a maximal contiguous degree can be modified to answer a question of Walk about the array computable degrees and a question of Li about isolated formulas. (shrink)

Soare [20] proved that the maximal sets form an orbit in${\cal E}$. We consider here${\cal D}$-maximal sets, generalizations of maximal sets introduced by Herrmann and Kummer [12]. Some orbits of${\cal D}$-maximal sets are well understood, e.g., hemimaximal sets [8], but many are not. The goal of this paper is to define new invariants on computably enumerable sets and to use them to give a complete nontrivial classification of the${\cal D}$-maximal sets. Although these invariants help us to better understand the${\cal D}$-maximal (...) sets, we use them to show that several classes of${\cal D}$-maximal sets break into infinitely many orbits. (shrink)

We prove conjectures of Herrmann and Stob by showing that the dense simple sets are orbit complete w.r.t. the simple sets.

Now in a third edition, Introduction to Philosophy: Classical and Contemporary Readings is a highly acclaimed, topically organized collection that covers five major areas of philosophy--theory of knowledge, philosophy of religion, philosophy of mind, freedom and determinism, and moral philosophy. Editor Louis P. Pojman enhances the text's topical organization by arranging the selections into a pro/con format to help students better understand opposing arguments. He also includes accessible introductions to each chapter, subsection, and individual reading, a unique feature for an (...) anthology of this depth. While the book focuses on a compelling sampling of classical material--including selections from Plato, Aristotle, Descartes, Locke, Berkeley, Hume, and Kant--it also incorporates some of philosophy's best twentieth-century and contemporary work, featuring articles by Bertrand Russell, Richard Taylor, John Searle, Thomas Nagel, and others. This third edition contains an expanded glossary, more extensive section introductions, and twelve new selections: Karl Popper: "Epistemology without a Knowing Subject" Richard Rorty: "Dismantling Truth: Solidarity Versus Objectivity" Daniel Dennett: "Postmodernism and Truth" Bruce Russell: "The Problem of Evil: Too Much Suffering" David Chalmers: "Against Materialism: Can Consciousness Be Reductively Explained?" Baron Paul Henri d'Holbach: "A Defense of Determinism" Michael Levin: "A Compatibilist Defense of Moral Responsibility" Plato: Socratic Morality: "Crito" Herodotus: "Custom Is King" J. L. Mackie: "The Subjectivity of Values" Louis P. Pojman: "A Critique of Mackie's Theory of Moral Subjectivism" Thomas Nagel: "Moral Luck". (shrink)

In ”Skepticism,” Peter Klein distinguishes between the “Academic Skeptic” who proposes that we cannot have knowledge of a certain set of propositions and the “Pyrrhonian Skeptic” who refrains from opining about whether we can have knowledge. Klein argues that Academic Skepticism is plausibly supported by a “Closure Principle‐style” argument based on the claim that if x entails y and S has justification for x, then S has justification for y. He turns to contextualism to see if it can contribute to (...) the discussion between one who claims that we can have knowledge about some epistemically interesting class of propositions and the Academic Skeptic. He outlines the background of Pyrrhonian Skepticism, pointing out that the Pyrrhonist withholds assent concerning our knowledge‐bearing status because reason cannot provide an adequate basis for assent. He assesses three possible patterns of reasoning, and concludes that the Pyrrhonist view, that reason cannot resolve matters concerning the nonevident, is vindicated. (shrink)

This paper advances the research on personalization of political communication by investigating whether this process of focusing on politicians instead of political issues plays a role on Twitter. Results of a content analysis of 5,530 tweets posted in the run-up to the German federal election provide evidence that Twitter communication refers more often to politicians than to issues. However, tweets containing personal characteristics about political leaders play only a marginal role. When distinguishing among different groups of actors on Twitter (journalists, (...) politicians, citizens), we find that citizens focus more on candidates than do journalists or politicians. Investigating the impact of a televised debate on Twitter communication, we observe that this person-centered event puts the focus on individual politicians instead of issues. (shrink)

Pekakak adalah salah satu tokoh yang memiliki pengetahuan mendalam dan perencanaan yang cermat. Saat fajar menyingsing, ia terlihat bertengger di atas pohon. Dengan kemampuan sempurna untuk mengontrol kecepatan penerbangan miliknya, seperti kapan harus memperlambat atau mempercepat, dia dapat dengan mudah menghitung cara optimal untuk menangkap ikan.

This article aims to read feminist new materialisms (Barad), together with ‘postulated’ linguistic or cultural primacy of Queer Theory (Butler), to show how both are engaged in similar critical-ethical endeavours. The central argument is that the criticism of Barad and new materialisms misses Butler’s materialistic insights due to a narrow interpretation of Butler's alleged social-constructivist position. There is, therefore, a specific focus on where they both make similar ethical appeals. Moreover, the article relies on Adorno's negative dialectic to highlight an (...) interpretation of Barad and Butler as being part of the same dialectical movement, in which materialism and idealism fluctuate in their mutual criticisms, thus continuing the procession towards 'new knowledge' and emancipation, or freedom, through their motions back and forth. (shrink)

Differential scanning calorimetry (DSC) has been employed to investigate the glass transition activation energy E g, thermal stability and glass-forming ability (GFA) of Se90In10− x Sb x (x = 0, 2, 4, 6, 8, 10) chalcogenide glasses. DSC runs were performed at six different heating rates. Well-defined endothermic and exothermic peaks were obtained at glass transition and crystallization temperature. The dependence of glass transition temperature T g on heating rate (α), as well as composition of Sb, has been studied. From (...) the dependence of glass transition temperature on heating rate, the E g has been calculated on the basis of the Kissinger [Anal. Chem. 29 (1957) p.1702] and Moynihan [J. Phys. Chem. 78 (1974) p.267] models. Thermal stability has been monitored through the calculation of temperature differences T c–T g, the stability parameter S, and the enthalpy released during crystallization H c. The GFA has been investigated on the basis of the Hruby parameter H r, which is strong indicator of GFA. Results for GFA are in good agreement with fragility index F i calculations, indicating that Se90In6Sb4 is an excellent glass-former. (shrink)

This book is an examination of the metaphysical systems of Margaret Cavendish and Anne Conway, who share many superficial similarities. By providing a detailed analysis of their views on substance, monism, self-motion, individuation, and identity over time, as well as causation, perception, and freedom, it demonstrates the interesting ways in which their accounts differ. Seeing their systems in tandem highlights the originality of each philosopher. In addition to providing the details of their metaphysical views, the book also shows how they (...) put these views to use: for Cavendish in grounding her natural philosophy and for Conway in developing her theodicy. The account of Cavendish is more naturalistic than current interpretations. It argues that God plays no substantive role in Cavendish’s philosophy. The book provides an account of Cavendish’s matter and her biological holism. It shows how sensitive and rational matter are expressed differently in different natural kinds. It provides the first account of Cavendish’s views on individuation and identity over time and a detailed account of her views on causation, arguing that nature is the only principal cause. The book also provides an account of Conway’s spiritual substance, arguing that it is a unique type of substance. It discusses Conway’s two types of motions and causation. In addition, a detailed account of her view of motion as a mode of body, and how it is transferred, is provided. Finally, the book concludes that Conway’s metaphysics and morality are inseparable and that she holds a type of perfectionism. (shrink)