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Kenneth Kunen The Foundations of Mathematics (Paperback) Logic S.
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Item specifics
- Condition
- Book Title
- The Foundations of Mathematics
- Title
- The Foundations of Mathematics
- ISBN-10
- 1904987141
- EAN
- 9781904987147
- ISBN
- 9781904987147
- Genre
- Science Nature & Math
- Topic
- Philosophy & Spirituality
- Release Date
- 08/09/2009
- Release Year
- 2009
- Country/Region of Manufacture
- GB
- Item Length
- 156mm
- Series
- Logic S.
- Publication Year
- 2009
- Type
- Textbook
- Format
- Paperback
- Language
- English
- Publication Name
- The Foundations of Mathematics
- Item Height
- 234mm
- Publisher
- College Publications
- Item Width
- 156mm
- Subject
- Mathematics
- Item Weight
- 372g
- Number of Pages
- 262 Pages
About this product
Product Information
Mathematical logic grew out of philosophical questions regarding the foundations of mathematics, but logic has now outgrown its philosophical roots, and has become an integral part of mathematics in general. This book is designed for students who plan to specialize in logic, as well as for those who are interested in the applications of logic to other areas of mathematics. Used as a text, it could form the basis of a beginning graduate-level course. There are three main chapters: Set Theory, Model Theory, and Recursion Theory. The Set Theory chapter describes the set-theoretic foundations of all of mathematics, based on the ZFC axioms. It also covers technical results about the Axiom of Choice, well-orderings, and the theory of uncountable cardinals. The Model Theory chapter discusses predicate logic and formal proofs, and covers the Completeness, Compactness, and Loewenheim-Skolem Theorems, elementary submodels, model completeness, and applications to algebra. This chapter also continues the foundational issues begun in the set theory chapter. Mathematics can now be viewed as formal proofs from ZFC. Also, model theory leads to models of set theory. This includes a discussion of absoluteness, and an analysis of models such as H( ) and R( ). The Recursion Theory chapter develops some basic facts about computable functions, and uses them to prove a number of results of foundational importance; in particular, Church's theorem on the undecidability of logical consequence, the incompleteness theorems of Goedel, and Tarski's theorem on the non-definability of truth.
Product Identifiers
Publisher
College Publications
ISBN-13
9781904987147
eBay Product ID (ePID)
103882495
Product Key Features
Publication Name
The Foundations of Mathematics
Format
Paperback
Language
English
Subject
Mathematics
Publication Year
2009
Type
Textbook
Number of Pages
262 Pages
Dimensions
Item Height
234mm
Item Width
156mm
Volume
V. 19
Item Weight
372g
Additional Product Features
Series Title
Logic S.
Topic
Popular Philosophy
Country/Region of Manufacture
United Kingdom
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