Cantorian Set Theory And Limitation Of Size
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Cantorian Set Theory And Limitation Of Size
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Author : Michael Hallett
language : en
Publisher: Oxford University Press
Release Date : 1986
Cantorian Set Theory And Limitation Of Size written by Michael Hallett and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1986 with Mathematics categories.
This volume presents the philosophical and heuristic framework Cantor developed and explores its lasting effect on modern mathematics. "Establishes a new plateau for historical comprehension of Cantor's monumental contribution to mathematics." --The American Mathematical Monthly
Cantorian Set Theory And Limitation Of Size
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Author : Michael Hallett
language : en
Publisher: Oxford University Press, USA
Release Date : 1984
Cantorian Set Theory And Limitation Of Size written by Michael Hallett and has been published by Oxford University Press, USA this book supported file pdf, txt, epub, kindle and other format this book has been release on 1984 with Business & Economics categories.
Cantor's ideas formed the basis for set theory and also for the mathematical treatment of the concept of infinity. The philosophical and heuristic framework he developed had a lasting effect on modern mathematics, and is the recurrent theme of this volume. Hallett explores Cantor's ideas and, in particular, their ramifications for Zermelo-Frankel set theory.
Set Theory Logic And Their Limitations
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Author : Moshe Machover
language : en
Publisher: Cambridge University Press
Release Date : 1996-05-23
Set Theory Logic And Their Limitations written by Moshe Machover and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996-05-23 with Mathematics categories.
This is an introduction to set theory and logic that starts completely from scratch. The text is accompanied by many methodological remarks and explanations. A rigorous axiomatic presentation of Zermelo-Fraenkel set theory is given, demonstrating how the basic concepts of mathematics have apparently been reduced to set theory. This is followed by a presentation of propositional and first-order logic. Concepts and results of recursion theory are explained in intuitive terms, and the author proves and explains the limitative results of Skolem, Tarski, Church and Gödel (the celebrated incompleteness theorems). For students of mathematics or philosophy this book provides an excellent introduction to logic and set theory.
The Foundations Of Mathematics In The Theory Of Sets
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Author : John P. Mayberry
language : en
Publisher: Cambridge University Press
Release Date : 2000
The Foundations Of Mathematics In The Theory Of Sets written by John P. Mayberry and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with Mathematics categories.
This book presents a unified approach to the foundations of mathematics in the theory of sets, covering both conventional and finitary (constructive) mathematics. It is based on a philosophical, historical and mathematical analysis of the relation between the concepts of 'natural number' and 'set'. The author investigates the logic of quantification over the universe of sets and discusses its role in second order logic, as well as in the analysis of proof by induction and definition by recursion. Suitable for graduate students and researchers in both philosophy and mathematics.
The Mystery Of The Aleph
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Author : Amir D. Aczel
language : en
Publisher: Simon and Schuster
Release Date : 2001-08-28
The Mystery Of The Aleph written by Amir D. Aczel and has been published by Simon and Schuster this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-08-28 with Mathematics categories.
A compelling narrative that blends the story of infinity with the tragic tale of a tormented and brilliant mathematician.
Everything More Or Less
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Author : J. P. Studd
language : en
Publisher: Oxford University Press
Release Date : 2019-04-04
Everything More Or Less written by J. P. Studd and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-04-04 with Philosophy categories.
Almost no systematic theorizing is generality-free. Scientists test general hypotheses; set theorists prove theorems about every set; metaphysicians espouse theses about all things regardless of their kind. But how general can we be and do we ever succeed in theorizing about absolutely everything? Not according to generality relativism. In its most promising form, this kind of relativism maintains that what 'everything' and other quantifiers encompass is always open to expansion: no matter how broadly we may generalize, a more inclusive 'everything' is always available. The importance of the issue comes out, in part, in relation to the foundations of mathematics. Generality relativism opens the way to avoid Russell's paradox without imposing ad hoc limitations on which pluralities of items may be encoded as a set. On the other hand, generality relativism faces numerous challenges: What are we to make of seemingly absolutely general theories? What prevents our achieving absolute generality simply by using 'everything' unrestrictedly? How are we to characterize relativism without making use of exactly the kind of generality this view foreswears? This book offers a sustained defence of generality relativism that seeks to answer these challenges. Along the way, the contemporary absolute generality debate is traced through diverse issues in metaphysics, logic, and the philosophy of language; some of the key works that lie behind the debate are reassessed; an accessible introduction is given to the relevant mathematics; and a relativist-friendly motivation for Zermelo-Fraenkel set theory is developed.
Conceptual Roots Of Mathematics
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Author : J.R. Lucas
language : en
Publisher: Routledge
Release Date : 2002-09-11
Conceptual Roots Of Mathematics written by J.R. Lucas and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-09-11 with Philosophy categories.
The Conceptual Roots of Mathematics is a comprehensive study of the foundation of mathematics. J.R. Lucas, one of the most distinguished Oxford scholars, covers a vast amount of ground in the philosophy of mathematics, showing us that it is actually at the heart of the study of epistemology and metaphysics.
Boolean Valued Analysis
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Author : A.G. Kusraev
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Boolean Valued Analysis written by A.G. Kusraev and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
Boolean valued analysis is a technique for studying properties of an arbitrary mathematical object by comparing its representations in two different set-theoretic models whose construction utilises principally distinct Boolean algebras. The use of two models for studying a single object is a characteristic of the so-called non-standard methods of analysis. Application of Boolean valued models to problems of analysis rests ultimately on the procedures of ascending and descending, the two natural functors acting between a new Boolean valued universe and the von Neumann universe. This book demonstrates the main advantages of Boolean valued analysis which provides the tools for transforming, for example, function spaces to subsets of the reals, operators to functionals, and vector-functions to numerical mappings. Boolean valued representations of algebraic systems, Banach spaces, and involutive algebras are examined thoroughly. Audience: This volume is intended for classical analysts seeking powerful new tools, and for model theorists in search of challenging applications of nonstandard models.
The Hyperuniverse Project And Maximality
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Author : Carolin Antos
language : en
Publisher: Birkhäuser
Release Date : 2018-01-30
The Hyperuniverse Project And Maximality written by Carolin Antos and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-01-30 with Mathematics categories.
This collection documents the work of the Hyperuniverse Project which is a new approach to set-theoretic truth based on justifiable principles and which leads to the resolution of many questions independent from ZFC. The contributions give an overview of the program, illustrate its mathematical content and implications, and also discuss its philosophical assumptions. It will thus be of wide appeal among mathematicians and philosophers with an interest in the foundations of set theory. The Hyperuniverse Project was supported by the John Templeton Foundation from January 2013 until September 2015
Interpolation And Definability
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Author : Dov M. Gabbay
language : en
Publisher: Clarendon Press
Release Date : 2005-05-12
Interpolation And Definability written by Dov M. Gabbay and has been published by Clarendon Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-05-12 with Mathematics categories.
This book is a specialized monograph on interpolation and definability, a notion central in pure logic and with significant meaning and applicability in all areas where logic is applied, especially computer science, artificial intelligence, logic programming, philosophy of science and natural language. Suitable for researchers and graduate students in mathematics, computer science and philosophy, this is the latest in the prestigous world-renowned Oxford Logic Guides, which contains Michael Dummet's Elements of intuitionism (second edition), J. M. Dunn and G. Hardegree's Algebraic Methods in Philosophical Logic, H. Rott's Change, Choice and Inference: A Study of Belief Revision and Nonmonotonic Reasoning, P. T. Johnstone's Sketches of an Elephant: A Topos Theory Compendium: Volumes 1 and 2, and David J. Pym and Eike Ritter's Reductive Logic and Proof Search: Proof theory, semantics and control.