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Author: Alexander Kechris
Publisher: Springer
ISBN:
Category : Mathematics
Languages : en
Pages : 238
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Book Description
This is the fourth volume of the proceeding of the Caltech-UCLA Logic Seminar, based mainly on material which was presented and discussed in the period 1981-85, but containing also some very recent results. It includes research papers dealing with determinacy hypotheses and their consequences in descriptive set theory. An appendix contains the new Victoria Delfino Problems.
Author: Alexander Kechris
Publisher: Springer
ISBN:
Category : Mathematics
Languages : en
Pages : 238
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Book Description
This is the fourth volume of the proceeding of the Caltech-UCLA Logic Seminar, based mainly on material which was presented and discussed in the period 1981-85, but containing also some very recent results. It includes research papers dealing with determinacy hypotheses and their consequences in descriptive set theory. An appendix contains the new Victoria Delfino Problems.
Author: Alexander S. Kechris
Publisher: Cambridge University Press
ISBN: 113950424X
Category : Mathematics
Languages : en
Pages : 549
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Book Description
The proceedings of the Los Angeles Caltech-UCLA 'Cabal Seminar' were originally published in the 1970s and 1980s. Wadge Degrees and Projective Ordinals is the second of a series of four books collecting the seminal papers from the original volumes together with extensive unpublished material, new papers on related topics and discussion of research developments since the publication of the original volumes. Focusing on the subjects of 'Wadge Degrees and Pointclasses' (Part III) and 'Projective Ordinals' (Part IV), each of the two sections is preceded by an introductory survey putting the papers into present context. These four volumes will be a necessary part of the book collection of every set theorist.
Author: Akihiro Kanamori
Publisher: Springer Science & Business Media
ISBN: 9783540003847
Category : Large cardinals (Mathematics)
Languages : en
Pages : 568
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Book Description
This is the softcover reprint of the very popular hardcover edition. The theory of large cardinals is currently a broad mainstream of modern set theory, the main area of investigation for the analysis of the relative consistency of mathematical propositions and possible new axioms for mathematics. The first of a projected multi-volume series, this book provides a comprehensive account of the theory of large cardinals from its beginnings and some of the direct outgrowths leading to the frontiers of contemporary research. A a oegenetica approach is taken, presenting the subject in the context of its historical development. With hindsight the consequential avenues are pursued and the most elegant or accessible expositions given. With open questions and speculations provided throughout the reader should not only come to appreciate the scope and coherence of the overall enterprise but also become prepared to pursue research in several specific areas by studying the relevant sections.
Author: Alexander S. Kechris
Publisher: Cambridge University Press
ISBN: 1316586286
Category : Mathematics
Languages : en
Pages : 552
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Book Description
The proceedings of the Los Angeles Caltech-UCLA 'Cabal Seminar' were originally published in the 1970s and 1980s. Ordinal Definability and Recursion Theory is the third in a series of four books collecting the seminal papers from the original volumes together with extensive unpublished material, new papers on related topics and discussion of research developments since the publication of the original volumes. Focusing on the subjects of 'HOD and its Local Versions' (Part V) and 'Recursion Theory' (Part VI), each of the two sections is preceded by an introductory survey putting the papers into present context. These four volumes will be a necessary part of the book collection of every set theorist.
Author: Paul B. Larson
Publisher: American Mathematical Society
ISBN: 1470472104
Category : Mathematics
Languages : en
Pages : 182
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Book Description
This is an expository account of work on strong forms of the Axiom of Determinacy (AD) by a group of set theorists in Southern California, in particular by W. Hugh Woodin. The first half of the book reviews necessary background material, including the Moschovakis Coding Lemma, the existence of strong partition cardinals, and the analysis of pointclasses in models of determinacy. The second half of the book introduces Woodin's axiom system $mathrm{AD}^{+}$ and presents his initial analysis of these axioms. These results include the consistency of $mathrm{AD}^{+}$ from the consistency of AD, and its local character and initial motivation. Proofs are given of fundamental results by Woodin, Martin, and Becker on the relationships among AD, $mathrm{AD}^{+}$, the Axiom of Real Determinacy, and the Suslin property. Many of these results are proved in print here for the first time. The book briefly discusses later work and fundamental questions which remain open. The study of models of $mathrm{AD}^{+}$ is an active area of contemporary research in set theory. The presentation is aimed at readers with a background in basic set theory, including forcing and ultrapowers. Some familiarity with classical results on regularity properties for sets of reals under AD is also expected.
Author: Alexander Kechris
Publisher: Springer Science & Business Media
ISBN: 1461241901
Category : Mathematics
Languages : en
Pages : 419
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Book Description
Descriptive set theory has been one of the main areas of research in set theory for almost a century. This text presents a largely balanced approach to the subject, which combines many elements of the different traditions. It includes a wide variety of examples, more than 400 exercises, and applications, in order to illustrate the general concepts and results of the theory.
Author: Benedikt Löwe
Publisher: Springer Science & Business Media
ISBN: 1402027761
Category : Computers
Languages : en
Pages : 266
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Book Description
The notion of complexity is an important contribution of logic to theoretical computer science and mathematics. This volume attempts to approach complexity in a holistic way, investigating mathematical properties of complexity hierarchies at the same time as discussing algorithms and computational properties. A main focus of the volume is on some of the new paradigms of computation, among them Quantum Computing and Infinitary Computation. The papers in the volume are tied together by an introductory article describing abstract properties of complexity hierarchies. This volume will be of great interest to both mathematical logicians and theoretical computer scientists, providing them with new insights into the various views of complexity and thus shedding new light on their own research.
Author: Harold G. Dales
Publisher: Oxford University Press
ISBN: 9780198514763
Category : Mathematics
Languages : en
Pages : 396
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Book Description
The nature of truth in mathematics has exercised the minds of thinkers from at least the time of the ancient Greeks. The great advances in mathematics and philosophy in the twentieth century and in particular the work by G]odel and the development of the notion of independence in mathematics have led to new and complex views on this question. Collecting the work of a number of outstanding mathematicians and philosophers, including Yurii Manin, Vaughan Jones, and Per Martin-L]of, this volume provides an overview of the forefront of current thinking and a valuable introduction for researchers in the area.
Author: David Marker
Publisher: Cambridge University Press
ISBN: 1316858081
Category : Mathematics
Languages : en
Pages : 192
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Book Description
Infinitary logic, the logic of languages with infinitely long conjunctions, plays an important role in model theory, recursion theory and descriptive set theory. This book is the first modern introduction to the subject in forty years, and will bring students and researchers in all areas of mathematical logic up to the threshold of modern research. The classical topics of back-and-forth systems, model existence techniques, indiscernibles and end extensions are covered before more modern topics are surveyed. Zilber's categoricity theorem for quasiminimal excellent classes is proved and an application is given to covers of multiplicative groups. Infinitary methods are also used to study uncountable models of counterexamples to Vaught's conjecture, and effective aspects of infinitary model theory are reviewed, including an introduction to Montalbán's recent work on spectra of Vaught counterexamples. Self-contained introductions to effective descriptive set theory and hyperarithmetic theory are provided, as is an appendix on admissible model theory.
Author: Peter Gärdenfors
Publisher: Springer Science & Business Media
ISBN: 9781402009297
Category : Computers
Languages : en
Pages : 414
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Book Description
This is the first of two volumes containing papers submitted by the invited speakers to the 11th International Congress of Logic, Methodology and Philosophy of Science, held in Cracow in 1999, under the auspices of the International Union of History and Philosophy of Science, Division of Logic, Methodology and Philosophy of Science. The invited speakers are the leading researchers and accordingly the book presents the current state of the intellectual discourse in the respective fields. The papers delivered at the congress were divided into 17 sections. Thus the structure of the volume corresponds to the very schedule of the congress. Volume one contains the opening lecture by Andrzej K. Wróblewski as well as invited papers in sections of Proof Theory, Model Theory, Recursion Theory, Axiomatic Set Theory, Logic and Computation, Logic, Language and Cognition, Methodology, Probability, Induction, and Decision Theory, Philosophy of Logic, Mathematics, and Computer Science, and Philosophy of the Physical Sciences.
