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Harvey Friedmans Research On The Foundations Of Mathematics
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Book Synopsis Harvey Friedman's Research on the Foundations of Mathematics by : L.A. Harrington
Download or read book Harvey Friedman's Research on the Foundations of Mathematics written by L.A. Harrington and published by Elsevier. This book was released on 1985-11-01 with total page 407 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume discusses various aspects of Harvey Friedman's research in the foundations of mathematics over the past fifteen years. It should appeal to a wide audience of mathematicians, computer scientists, and mathematically oriented philosophers.
Book Synopsis Foundational Adventures by : Neil Tennant
Download or read book Foundational Adventures written by Neil Tennant and published by . This book was released on 2014-01 with total page 314 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is a tribute by his peers, and by younger scholars of the next generation, to Harvey M. Friedman, perhaps the most profound foundationalist since Kurt Godel. Friedman's researches, beginning precociously in his mid-teens, have fundamentally shaped our contemporary understanding of set theory, recursion theory, model theory, proof theory and metamathematics. His achievements in concept formation and theory formulation have also renewed the standard set by Godel and Alfred Tarski for the general intellectual interest and importance of technical work in foundations. Friedman pioneered the now well-established and flourishing field of Reverse Mathematics, whose aim is to calibrate the intrinsic logico-mathematical consistency-strength of all the important theorems of mathematics. He has relentlessly pursued the full extent of the incompleteness phenomena into which Godel provided the first revealing glimpse. The Godel--Friedman program, as it is now deservingly called, seeks to find simple, natural and elegant mathematical statements of a combinatorial nature, that can be proved to be independent of set theory even when extended by powerful large-cardinal existence axioms.
Book Synopsis Reflections on the Foundations of Mathematics: Essays in Honor of Solomon Feferman by : Wilfried Sieg
Download or read book Reflections on the Foundations of Mathematics: Essays in Honor of Solomon Feferman written by Wilfried Sieg and published by CRC Press. This book was released on 2002-08-16 with total page 458 pages. Available in PDF, EPUB and Kindle. Book excerpt: Solomon Feferman has shaped the field of foundational research for nearly half a century. These papers, most of which were presented at the symposium honoring him at his 70th birthday, reflect his broad interests as well as his approach to foundational research, which places the solution of mathematical and philosophical problems at the top of his
Book Synopsis Reflections on the Foundations of Mathematics by : Wilfried Sieg
Download or read book Reflections on the Foundations of Mathematics written by Wilfried Sieg and published by Cambridge University Press. This book was released on 2017-03-30 with total page 456 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since their inception, the Perspectives in Logic and Lecture Notes in Logic series have published seminal works by leading logicians. Many of the original books in the series have been unavailable for years, but they are now in print once again. This volume, the fifteenth publication in the Lecture Notes in Logic series, collects papers presented at the symposium 'Reflections on the Foundations of Mathematics' held in celebration of Solomon Feferman's 70th birthday (The 'Feferfest') at Stanford University, California in 1988. Feferman has shaped the field of foundational research for nearly half a century. These papers reflect his broad interests as well as his approach to foundational research, which emphasizes the solution of mathematical and philosophical problems. There are four sections, covering proof theoretic analysis, logic and computation, applicative and self-applicative theories, and philosophy of modern mathematical and logic thought.
Book Synopsis Mathematics and Its Logics by : Geoffrey Hellman
Download or read book Mathematics and Its Logics written by Geoffrey Hellman and published by Cambridge University Press. This book was released on 2021-02-04 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt: In these essays Geoffrey Hellman presents a strong case for a healthy pluralism in mathematics and its logics, supporting peaceful coexistence despite what appear to be contradictions between different systems, and positing different frameworks serving different legitimate purposes. The essays refine and extend Hellman's modal-structuralist account of mathematics, developing a height-potentialist view of higher set theory which recognizes indefinite extendability of models and stages at which sets occur. In the first of three new essays written for this volume, Hellman shows how extendability can be deployed to derive the axiom of Infinity and that of Replacement, improving on earlier accounts; he also shows how extendability leads to attractive, novel resolutions of the set-theoretic paradoxes. Other essays explore advantages and limitations of restrictive systems - nominalist, predicativist, and constructivist. Also included are two essays, with Solomon Feferman, on predicative foundations of arithmetic.
Book Synopsis Mathematical Logic by : Petio P. Petkov
Download or read book Mathematical Logic written by Petio P. Petkov and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 405 pages. Available in PDF, EPUB and Kindle. Book excerpt: Heyting'88 Summer School and Conference on Mathematical Logic, held September 13 - 23, 1988 in Chaika, Bulgaria, was honourably dedicated to Arend Heyting's 90th anniversary. It was organized by Sofia University "Kliment Ohridski" on the occasion of its centenary and by the Bulgarian Academy of Sciences, with sponsorship of the Association for Symbolic Logic. The Meeting gathered some 115 participants from 19 countries. The present volume consists of invited and selected papers. Included are all the invited lectures submitted for publication and the 14 selected contributions, chosen out of 56 submissions by the Selection Committee. The selection was made on the basis of reports of PC members, an average of 4 per sLlbmission. All the papers are concentrated on the topics of the Meeting: Recursion Theory, Modal and Non-classical Logics, Intuitionism and Constructivism, Related Applications to Computer and Other Sciences, Life and Work of Arend Heyting. I am pleased to thank all persons and institutions that contributed to the success of the Meeting: sponsors, Programme Committee members and additional referees, the members of the Organizing Committee, our secretaries K. Lozanova and L. Nikolova, as well as K. Angelov, V. Bozhichkova, A. Ditchev, D. Dobrev, N. Dimitrov, R. Draganova, G. Gargov, N. Georgieva, M. Janchev, P. Marinov, S. Nikolova, S. Radev, I. Soskov, A. Soskova and v. Sotirov, who helped in the organization, Plenum Press and at last but not least all participants in the Meeting and contributors to this volume
Book Synopsis Routledge Encyclopedia of Philosophy: Genealogy to Iqbal by : Edward Craig
Download or read book Routledge Encyclopedia of Philosophy: Genealogy to Iqbal written by Edward Craig and published by Taylor & Francis. This book was released on 1998 with total page 896 pages. Available in PDF, EPUB and Kindle. Book excerpt: Volume four of a ten volume set which provides full and detailed coverage of all aspects of philosophy, including information on how philosophy is practiced in different countries, who the most influential philosophers were, and what the basic concepts are.
Book Synopsis Infinity And Truth by : Chi Tat Chong
Download or read book Infinity And Truth written by Chi Tat Chong and published by World Scientific. This book was released on 2013-11-28 with total page 245 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is based on the talks given at the Workshop on Infinity and Truth held at the Institute for Mathematical Sciences, National University of Singapore, from 25 to 29 July 2011. The chapters cover topics in mathematical and philosophical logic that examine various aspects of the foundations of mathematics. The theme of the volume focuses on two basic foundational questions: (i) What is the nature of mathematical truth and how does one resolve questions that are formally unsolvable within the Zermelo-Fraenkel Set Theory with the Axiom of Choice, and (ii) Do the discoveries in mathematics provide evidence favoring one philosophical view over others? These issues are discussed from the vantage point of recent progress in foundational studies.The final chapter features questions proposed by the participants of the Workshop that will drive foundational research. The wide range of topics covered here will be of interest to students, researchers and mathematicians concerned with issues in the foundations of mathematics.
Book Synopsis Model Theory and the Philosophy of Mathematical Practice by : John T. Baldwin
Download or read book Model Theory and the Philosophy of Mathematical Practice written by John T. Baldwin and published by Cambridge University Press. This book was released on 2018-01-25 with total page 365 pages. Available in PDF, EPUB and Kindle. Book excerpt: Major shifts in the field of model theory in the twentieth century have seen the development of new tools, methods, and motivations for mathematicians and philosophers. In this book, John T. Baldwin places the revolution in its historical context from the ancient Greeks to the last century, argues for local rather than global foundations for mathematics, and provides philosophical viewpoints on the importance of modern model theory for both understanding and undertaking mathematical practice. The volume also addresses the impact of model theory on contemporary algebraic geometry, number theory, combinatorics, and differential equations. This comprehensive and detailed book will interest logicians and mathematicians as well as those working on the history and philosophy of mathematics.
Book Synopsis Philosophy of Science, Logic and Mathematics in the 20th Century by : Stuart G. Shanker
Download or read book Philosophy of Science, Logic and Mathematics in the 20th Century written by Stuart G. Shanker and published by Taylor & Francis. This book was released on 2023-05-09 with total page 500 pages. Available in PDF, EPUB and Kindle. Book excerpt: The twentieth century witnessed the birth of analytic philosophy. This volume covers some of its key movements and philosophers, including Frege and Wittgenstein's Tractatus.
Book Synopsis Well-Quasi Orders in Computation, Logic, Language and Reasoning by : Peter M. Schuster
Download or read book Well-Quasi Orders in Computation, Logic, Language and Reasoning written by Peter M. Schuster and published by Springer Nature. This book was released on 2020-01-01 with total page 391 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book bridges the gaps between logic, mathematics and computer science by delving into the theory of well-quasi orders, also known as wqos. This highly active branch of combinatorics is deeply rooted in and between many fields of mathematics and logic, including proof theory, commutative algebra, braid groups, graph theory, analytic combinatorics, theory of relations, reverse mathematics and subrecursive hierarchies. As a unifying concept for slick finiteness or termination proofs, wqos have been rediscovered in diverse contexts, and proven to be extremely useful in computer science. The book introduces readers to the many facets of, and recent developments in, wqos through chapters contributed by scholars from various fields. As such, it offers a valuable asset for logicians, mathematicians and computer scientists, as well as scholars and students.
Book Synopsis From Sets and Types to Topology and Analysis by : Laura Crosilla
Download or read book From Sets and Types to Topology and Analysis written by Laura Crosilla and published by Clarendon Press. This book was released on 2005-10-06 with total page 372 pages. Available in PDF, EPUB and Kindle. Book excerpt: This edited collection bridges the foundations and practice of constructive mathematics and focusses on the contrast between the theoretical developments, which have been most useful for computer science (eg constructive set and type theories), and more specific efforts on constructive analysis, algebra and topology. Aimed at academic logicians, mathematicians, philosophers and computer scientists Including, with contributions from leading researchers, it is up-to-date, highly topical and broad in scope. This is the latest volume in the Oxford Logic Guides, which also includes: 41. J.M. Dunn and G. Hardegree: Algebraic Methods in Philosophical Logic 42. H. Rott: Change, Choice and Inference: A study of belief revision and nonmonotoic reasoning 43. Johnstone: Sketches of an Elephant: A topos theory compendium, volume 1 44. Johnstone: Sketches of an Elephant: A topos theory compendium, volume 2 45. David J. Pym and Eike Ritter: Reductive Logic and Proof Search: Proof theory, semantics and control 46. D.M. Gabbay and L. Maksimova: Interpolation and Definability: Modal and Intuitionistic Logics 47. John L. Bell: Set Theory: Boolean-valued models and independence proofs, third edition
Book Synopsis A Tour Through Mathematical Logic by : Robert S. Wolf
Download or read book A Tour Through Mathematical Logic written by Robert S. Wolf and published by American Mathematical Soc.. This book was released on 2005-12-31 with total page 397 pages. Available in PDF, EPUB and Kindle. Book excerpt: A Tour Through Mathematical Logic provides a tour through the main branches of the foundations of mathematics. It contains chapters covering elementary logic, basic set theory, recursion theory, Gödel's (and others') incompleteness theorems, model theory, independence results in set theory, nonstandard analysis, and constructive mathematics. In addition, this monograph discusses several topics not normally found in books of this type, such as fuzzy logic, nonmonotonic logic, and complexity theory.
Book Synopsis Set Theory of the Continuum by : Haim Judah
Download or read book Set Theory of the Continuum written by Haim Judah and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 417 pages. Available in PDF, EPUB and Kindle. Book excerpt: Primarily consisting of talks presented at a workshop at the MSRI during its "Logic Year" 1989-90, this volume is intended to reflect the whole spectrum of activities in set theory. The first section of the book comprises the invited papers surveying the state of the art in a wide range of topics of set-theoretic research. The second section includes research papers on various aspects of set theory and its relation to algebra and topology. Contributors include: J.Bagaria, T. Bartoszynski, H. Becker, P. Dehornoy, Q. Feng, M. Foreman, M. Gitik, L. Harrington, S. Jackson, H. Judah, W. Just, A.S. Kechris, A. Louveau, S. MacLane, M. Magidor, A.R.D. Mathias, G. Melles, W.J. Mitchell, S. Shelah, R.A. Shore, R.I. Soare, L.J. Stanley, B. Velikovic, H. Woodin.
Book Synopsis Logic Colloquium '87 by : Heinz-Dieter Ebbinghaus
Download or read book Logic Colloquium '87 written by Heinz-Dieter Ebbinghaus and published by Elsevier. This book was released on 1989 with total page 387 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fourteen papers presented at the 1987 European Summer Meeting of the Association for Symbolic Logic are collected in this volume. The main areas covered by the conference were Logic, Set Theory, Recursion Theory, Model Theory, Logic for Computer Science and Semantics of Natural Languages.
Book Synopsis Logic Colloquium '87 by : H.-D. Ebbinghaus
Download or read book Logic Colloquium '87 written by H.-D. Ebbinghaus and published by Elsevier. This book was released on 2000-04-01 with total page 387 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fourteen papers presented at the 1987 European Summer Meeting of the Association for Symbolic Logic are collected in this volume.The main areas covered by the conference were Logic, Set Theory, Recursion Theory, Model Theory, Logic for Computer Science and Semantics of Natural Languages.
Book Synopsis Logical Methods by : John N. Crossley
Download or read book Logical Methods written by John N. Crossley and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 829 pages. Available in PDF, EPUB and Kindle. Book excerpt: The twenty-six papers in this volume reflect the wide and still expanding range of Anil Nerode's work. A conference on Logical Methods was held in honor of Nerode's sixtieth birthday (4 June 1992) at the Mathematical Sciences Institute, Cornell University, 1-3 June 1992. Some of the conference papers are here, but others are from students, co-workers and other colleagues. The intention of the conference was to look forward, and to see the directions currently being pursued, in the development of work by, or with, Nerode. Here is a brief summary of the contents of this book. We give a retrospective view of Nerode's work. A number of specific areas are readily discerned: recursive equivalence types, recursive algebra and model theory, the theory of Turing degrees and r.e. sets, polynomial-time computability and computer science. Nerode began with automata theory and has also taken a keen interest in the history of mathematics. All these areas are represented. The one area missing is Nerode's applied mathematical work relating to the environment. Kozen's paper builds on Nerode's early work on automata. Recursive equivalence types are covered by Dekker and Barback, the latter using directly a fundamental metatheorem of Nerode. Recursive algebra is treated by Ge & Richards (group representations). Recursive model theory is the subject of papers by Hird, Moses, and Khoussainov & Dadajanov, while a combinatorial problem in recursive model theory is discussed in Cherlin & Martin's paper. Cenzer presents a paper on recursive dynamics.
