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Author: Lorenz Halbeisen
Publisher: Springer Nature
ISBN: 3030522792
Category : Mathematics
Languages : en
Pages : 236
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Book Description
This book provides a concise and self-contained introduction to the foundations of mathematics. The first part covers the fundamental notions of mathematical logic, including logical axioms, formal proofs and the basics of model theory. Building on this, in the second and third part of the book the authors present detailed proofs of Gödel’s classical completeness and incompleteness theorems. In particular, the book includes a full proof of Gödel’s second incompleteness theorem which states that it is impossible to prove the consistency of arithmetic within its axioms. The final part is dedicated to an introduction into modern axiomatic set theory based on the Zermelo’s axioms, containing a presentation of Gödel’s constructible universe of sets. A recurring theme in the whole book consists of standard and non-standard models of several theories, such as Peano arithmetic, Presburger arithmetic and the real numbers. The book addresses undergraduate mathematics students and is suitable for a one or two semester introductory course into logic and set theory. Each chapter concludes with a list of exercises.
Author: Lorenz Halbeisen
Publisher: Springer Nature
ISBN: 3030522792
Category : Mathematics
Languages : en
Pages : 236
Get Book
Book Description
This book provides a concise and self-contained introduction to the foundations of mathematics. The first part covers the fundamental notions of mathematical logic, including logical axioms, formal proofs and the basics of model theory. Building on this, in the second and third part of the book the authors present detailed proofs of Gödel’s classical completeness and incompleteness theorems. In particular, the book includes a full proof of Gödel’s second incompleteness theorem which states that it is impossible to prove the consistency of arithmetic within its axioms. The final part is dedicated to an introduction into modern axiomatic set theory based on the Zermelo’s axioms, containing a presentation of Gödel’s constructible universe of sets. A recurring theme in the whole book consists of standard and non-standard models of several theories, such as Peano arithmetic, Presburger arithmetic and the real numbers. The book addresses undergraduate mathematics students and is suitable for a one or two semester introductory course into logic and set theory. Each chapter concludes with a list of exercises.
Author: Gregory H. Moore
Publisher: Courier Corporation
ISBN: 0486488411
Category : Mathematics
Languages : en
Pages : 450
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Book Description
"This book chronicles the work of mathematician Ernst Zermelo (1871-1953) and his development of set theory's crucial principle, the axiom of choice. It covers the axiom's formulation during the early 20th century, the controversy it engendered, and its current central place in set theory and mathematical logic. 1982 edition"--
Author: Wucius Wong
Publisher: John Wiley & Sons
ISBN: 9780471285526
Category : Design
Languages : en
Pages : 356
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Book Description
An unprecedented package that gives readers the content of three important references by one of today's most influential design writers. This is a master class in the principles and practical fundamentals of design that will appeal to a broad audience of graphic artists and designers.
Author: Grzegorz Tomkowicz
Publisher: Cambridge University Press
ISBN: 1107042593
Category : Mathematics
Languages : en
Pages : 367
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Book Description
The Banach-Tarski Paradox seems patently false. The authors explain it and its implications in terms appropriate for an undergraduate.
Author:
Publisher:
ISBN:
Category : Logic, Symbolic and mathematical
Languages : en
Pages : 92
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Book Description
Author: Alfred North Whitehead
Publisher:
ISBN:
Category : Logic, Symbolic and mathematical
Languages : en
Pages : 688
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Author: J. Peregrin
Publisher: Springer Science & Business Media
ISBN: 9401592330
Category : Philosophy
Languages : en
Pages : 221
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Book Description
The question how to turn the principles implicitly governing the concept of truth into an explicit definition (or explication) of the concept hence coalesced with the question how to get a finite grip on the infinity of T-sentences. Tarski's famous and ingenious move was to introduce a new concept, satisfaction, which could be, on the one hand, recursively defined, and which, on the other hand, straightforwardly yielded an explication of truth. A surprising 'by-product' of Tarski's effort to bring truth under control was the breathtaking finding that truth is in a precisely defined sense ineffable, that no non trivial language can contain a truth-predicate which would be adequate for the very 4 language . This implied that truth (and consequently semantic concepts to which truth appeared to be reducible) proved itself to be strangely 'language-dependent': we can have a concept of truth-in-L for any language L, but we cannot have a concept of truth applicable to every language. In a sense, this means, as Quine (1969, p. 68) put it, that truth belongs to "transcendental metaphysics", and Tarski's 'scientific' investigations seem to lead us back towards a surprising proximity of some more traditional philosophical views on truth. 3. TARSKI'S THEORY AS A PARADIGM So far Tarski himself. Subsequent philosophers then had to find out what his considerations of the concept of truth really mean and what are their consequences; and this now seems to be an almost interminable task.
Author: Wucius Wong
Publisher: John Wiley & Sons
ISBN: 9780471287087
Category : Architecture
Languages : en
Pages : 230
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Book Description
Principles of Color Design, Second Edition, continues to provide the beginner with a foundation to develop a personal color sense. Written by Wucius Wong, an internationally recognized fine artist and authority in the design field, this classic book presents principles, theories, and applications simply and elegantly.
Author: Tobias Dantzig
Publisher:
ISBN:
Category : Arithmetic
Languages : en
Pages : 368
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Book Description
Author: K. J. Devlin
Publisher: Springer
ISBN: 354037034X
Category : Mathematics
Languages : en
Pages : 105
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Book Description
