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The Notre Dame Lectures

The Notre Dame Lectures Author Peter Cholak
ISBN-10 1568812493
Release 2005-04-09
Pages 200
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In fall 2000, the Notre Dame logic community hosted Greg Hjorth, Rodney G. Downey, Zoé Chatzidakis, and Paola D'Aquino as visiting lecturers. Each of them presented a month long series of expository lectures at the graduate level. The articles in this volume are refinements of these excellent lectures.

Logic Colloquium 2006

Logic Colloquium 2006 Author S. Barry Cooper
ISBN-10 9780521110815
Release 2009-09-07
Pages 373
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The 2006 proceedings from the Annual European Meeting of the Association for Symbolic Logic, also known as the Logic Colloquium.

Invariant Descriptive Set Theory

Invariant Descriptive Set Theory Author Su Gao
ISBN-10 158488794X
Release 2008-09-03
Pages 392
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Presents Results from a Very Active Area of Research Exploring an active area of mathematics that studies the complexity of equivalence relations and classification problems, Invariant Descriptive Set Theory presents an introduction to the basic concepts, methods, and results of this theory. It brings together techniques from various areas of mathematics, such as algebra, topology, and logic, which have diverse applications to other fields. After reviewing classical and effective descriptive set theory, the text studies Polish groups and their actions. It then covers Borel reducibility results on Borel, orbit, and general definable equivalence relations. The author also provides proofs for numerous fundamental results, such as the Glimm–Effros dichotomy, the Burgess trichotomy theorem, and the Hjorth turbulence theorem. The next part describes connections with the countable model theory of infinitary logic, along with Scott analysis and the isomorphism relation on natural classes of countable models, such as graphs, trees, and groups. The book concludes with applications to classification problems and many benchmark equivalence relations. By illustrating the relevance of invariant descriptive set theory to other fields of mathematics, this self-contained book encourages readers to further explore this very active area of research.

Computation and Logic in the Real World

Computation and Logic in the Real World Author S. Barry Cooper
ISBN-10 3540730001
Release 2007-06-11
Pages 826
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This book constitutes the refereed proceedings of the Third International Conference on Computability in Europe, CiE 2007, held in Sienna, Italy, in June 2007. The 50 revised full papers presented together with 36 invited papers were carefully reviewed and selected from 167 submissions.

Algorithmic Randomness and Complexity

Algorithmic Randomness and Complexity Author Rodney G. Downey
ISBN-10 9780387684413
Release 2010-10-29
Pages 855
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Computability and complexity theory are two central areas of research in theoretical computer science. This book provides a systematic, technical development of "algorithmic randomness" and complexity for scientists from diverse fields.

Formalism and Beyond

Formalism and Beyond Author Godehard Link
ISBN-10 9781614519966
Release 2014-10-09
Pages 430
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The essays collected in this volume focus on the role of formalist aspects in mathematical theorizing and practice, examining issues such as infinity, finiteness, and proof procedures, as well as central historical figures in the field, including Frege, Russell, Hilbert and Wittgenstein. Using modern logico-philosophical tools and systematic conceptual and logical analyses, the volume provides a thorough, up-to-date account of the subject.

Philosophy of Mathematics

Philosophy of Mathematics Author Gerhard Preyer
ISBN-10 9783110323689
Release 2008-01-01
Pages 184
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One main interest of philosophy is to become clear about the assumptions, premisses and inconsistencies of our thoughts and theories. And even for a formal language like mathematics it is controversial if consistency is acheivable or necessary like the articles in the firt part of the publication show. Also the role of formal derivations, the role of the concept of apriority, and the intuitions of mathematical principles and properties need to be discussed. The second part is a contribution on nominalistic and platonistic views in mathematics, like the "indispensability argument" of W. v. O. Quine H. Putnam and the "makes no difference argument" of A. Baker. Not only in retrospect, the third part shows the problems of Mill, Frege's and the unity of mathematics and Descartes's contradictional conception of mathematical essences. Together, these articles give us a hint into the relationship between mathematics and world, that is, one of the central problems in philosophy of mathematics and philosophy of science.

Computability and Complexity

Computability and Complexity Author Adam Day
ISBN-10 9783319500621
Release 2016-11-30
Pages 755
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This Festschrift is published in honor of Rodney G. Downey, eminent logician and computer scientist, surfer and Scottish country dancer, on the occasion of his 60th birthday. The Festschrift contains papers and laudations that showcase the broad and important scientific, leadership and mentoring contributions made by Rod during his distinguished career. The volume contains 42 papers presenting original unpublished research, or expository and survey results in Turing degrees, computably enumerable sets, computable algebra, computable model theory, algorithmic randomness, reverse mathematics, and parameterized complexity, all areas in which Rod Downey has had significant interests and influence. The volume contains several surveys that make the various areas accessible to non-specialists while also including some proofs that illustrate the flavor of the fields.

The Bulletin of Symbolic Logic

The Bulletin of Symbolic Logic Author
ISBN-10 UOM:39015059001266
Release 2006
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The Bulletin of Symbolic Logic has been writing in one form or another for most of life. You can find so many inspiration from The Bulletin of Symbolic Logic also informative, and entertaining. Click DOWNLOAD or Read Online button to get full The Bulletin of Symbolic Logic book for free.

Theory and Applications of Models of Computation

Theory and Applications of Models of Computation Author Jin-Yi Cai
ISBN-10 9783540340225
Release 2006-05-05
Pages 800
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This book constitutes the refereed proceedings of the Third International Conference on Theory and Applications of Models of Computation, TAMC 2006, held in Beijing, China, in May 2006. The 75 revised full papers presented together with 7 plenary talks were carefully reviewed and selected from 319 submissions. All major areas in computer science, mathematics (especially logic) and the physical sciences particularly with regard to computation and computability theory are addressed.

Logic Colloquium 2005

Logic Colloquium 2005 Author Costas Dimitracopoulos
ISBN-10 9780521884259
Release 2008
Pages 272
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This 2007 volume includes surveys, tutorials, and selected research papers on advances in logic.

Computational Prospects of Infinity Presented talks

Computational Prospects of Infinity  Presented talks Author Chi-Tat Chong
ISBN-10 9789812796547
Release 2008
Pages 420
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This volume is a collection of written versions of the talks given at the Workshop on Computational Prospects of Infinity, held at the Institute for Mathematical Sciences from 18 June to 15 August 2005. It consists of contributions from many of the leading experts in recursion theory (computability theory) and set theory. Topics covered include the structure theory of various notions of degrees of unsolvability, algorithmic randomness, reverse mathematics, forcing, large cardinals and inner model theory, and many others.

Computational Prospects of Infinity Part I

Computational Prospects of Infinity   Part I Author Chi-Tat Chong
ISBN-10 9789812794055
Release 2008
Pages 253
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This volume presents the written versions of the tutorial lectures given at the Workshop on Computational Prospects of Infinity, held from 18 June to 15 August 2005 at the Institute for Mathematical Sciences, National University of Singapore. It consists of articles by four of the leading experts in recursion theory (computability theory) and set theory. The survey paper of Rod Downey provides a comprehensive introduction to algorithmic randomness, one of the most active areas of current research in recursion theory. Theodore A Slaman's article is the first printed account of the ground-breaking work of Slaman-Woodin and Slaman-Shore on the definability of the Turing jump. John Steel presents some results on the properties of derived models of mice, and on the existence of mice with large derived models. The study was motivated by some of the well-known Holy Grails in inner model theory, including the Mouse Set Conjecture. In his presentation, W Hugh Woodin gives an outline of an expanded version (unpublished) on suitable extender sequences, a subject that was developed in the attempt to understand inner model theory for large cardinals beyond the level of superstrong cardinals. The volume serves as a useful guide for graduate students and researchers in recursion theory and set theory to some of the most important and significant developments in these subjects in recent years.

Computational Prospects of Infinity

Computational Prospects of Infinity Author
ISBN-10 9789814471596
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Computational Prospects of Infinity has been writing in one form or another for most of life. You can find so many inspiration from Computational Prospects of Infinity also informative, and entertaining. Click DOWNLOAD or Read Online button to get full Computational Prospects of Infinity book for free.

Residuated Lattices An Algebraic Glimpse at Substructural Logics

Residuated Lattices  An Algebraic Glimpse at Substructural Logics Author Nikolaos Galatos
ISBN-10 0080489648
Release 2007-04-25
Pages 532
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The book is meant to serve two purposes. The first and more obvious one is to present state of the art results in algebraic research into residuated structures related to substructural logics. The second, less obvious but equally important, is to provide a reasonably gentle introduction to algebraic logic. At the beginning, the second objective is predominant. Thus, in the first few chapters the reader will find a primer of universal algebra for logicians, a crash course in nonclassical logics for algebraists, an introduction to residuated structures, an outline of Gentzen-style calculi as well as some titbits of proof theory - the celebrated Hauptsatz, or cut elimination theorem, among them. These lead naturally to a discussion of interconnections between logic and algebra, where we try to demonstrate how they form two sides of the same coin. We envisage that the initial chapters could be used as a textbook for a graduate course, perhaps entitled Algebra and Substructural Logics. As the book progresses the first objective gains predominance over the second. Although the precise point of equilibrium would be difficult to specify, it is safe to say that we enter the technical part with the discussion of various completions of residuated structures. These include Dedekind-McNeille completions and canonical extensions. Completions are used later in investigating several finiteness properties such as the finite model property, generation of varieties by their finite members, and finite embeddability. The algebraic analysis of cut elimination that follows, also takes recourse to completions. Decidability of logics, equational and quasi-equational theories comes next, where we show how proof theoretical methods like cut elimination are preferable for small logics/theories, but semantic tools like Rabin's theorem work better for big ones. Then we turn to Glivenko's theorem, which says that a formula is an intuitionistic tautology if and only if its double negation is a classical one. We generalise it to the substructural setting, identifying for each substructural logic its Glivenko equivalence class with smallest and largest element. This is also where we begin investigating lattices of logics and varieties, rather than particular examples. We continue in this vein by presenting a number of results concerning minimal varieties/maximal logics. A typical theorem there says that for some given well-known variety its subvariety lattice has precisely such-and-such number of minimal members (where values for such-and-such include, but are not limited to, continuum, countably many and two). In the last two chapters we focus on the lattice of varieties corresponding to logics without contraction. In one we prove a negative result: that there are no nontrivial splittings in that variety. In the other, we prove a positive one: that semisimple varieties coincide with discriminator ones. Within the second, more technical part of the book another transition process may be traced. Namely, we begin with logically inclined technicalities and end with algebraically inclined ones. Here, perhaps, algebraic rendering of Glivenko theorems marks the equilibrium point, at least in the sense that finiteness properties, decidability and Glivenko theorems are of clear interest to logicians, whereas semisimplicity and discriminator varieties are universal algebra par exellence. It is for the reader to judge whether we succeeded in weaving these threads into a seamless fabric.

Automated Deduction CADE 18

Automated Deduction   CADE 18 Author Andrei Voronkov
ISBN-10 9783540456209
Release 2003-08-02
Pages 540
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The First CADE in the Third Millennium This volume contains the papers presented at the Eighteenth International C- ference on Automated Deduction (CADE-18) held on July 27–30th, 2002, at the University of Copenhagen as part of the Federated Logic Conference (FLoC 2002). Despite a large number of deduction-related conferences springing into existence at the end of the last millennium, the CADE conferences continue to be the major forum for the presentation of new research in all aspects of automated deduction. CADE-18 was sponsored by the Association for Auto- ted Reasoning, CADE Inc., the Department of Computer Science at Chalmers University, the Gesellschaft fur ̈ Informatik, Safelogic AB, and the University of Koblenz-Landau. There were 70 submissions, including 60 regular papers and 10 system - scriptions. Each submission was reviewed by at least ?ve program committee members and an electronic program committee meeting was held via the Int- net. The committee decided to accept 27 regular papers and 9 system descr- tions. One paper switched its category after refereeing, thus the total number of system descriptions in this volume is 10. In addition to the refereed papers, this volume contains an extended abstract of the CADE invited talk by Ian Horrocks, the joint CADE/CAV invited talk by Sharad Malik, and the joint CADE-TABLEAUX invited talk by Matthias Baaz. One more invited lecture was given by Daniel Jackson.

Basic Proof Theory

Basic Proof Theory Author A. S. Troelstra
ISBN-10 0521779111
Release 2000-07-27
Pages 417
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Introduction to proof theory and its applications in mathematical logic, theoretical computer science and artificial intelligence.