A thorough, accessible, and rigorous presentation of the central
theorems of mathematical logic . . . ideal for advanced students of
mathematics, computer science, and logic
Logic of Mathematics combines a full-scale introductory course in
mathematical logic and model theory with a range of specially
selected, more advanced theorems. Using a strict mathematical
approach, this is the only book available that contains complete
and precise proofs of all of these important theorems:
* GAdel's theorems of completeness and incompleteness
* The independence of Goodstein's theorem from Peano
arithmetic
* Tarski's theorem on real closed fields
* Matiyasevich's theorem on diophantine formulas
Logic of Mathematics also features:
* Full coverage of model theoretical topics such as definability,
compactness, ultraproducts, realization, and omission of
types
* Clear, concise explanations of all key concepts, from Boolean
algebras to Skolem-LAwenheim constructions and other topics
* Carefully chosen exercises for each chapter, plus helpful
solution hints
At last, here is a refreshingly clear, concise, and mathematically
rigorous presentation of the basic concepts of mathematical
logic-requiring only a standard familiarity with abstract algebra.
Employing a strict mathematical approach that emphasizes relational
structures over logical language, this carefully organized text is
divided into two parts, which explain the essentials of the subject
in specific and straightforward terms.
Part I contains a thorough introduction to mathematical logic and
model theory-including a full discussion of terms, formulas, and
other fundamentals, plus detailed coverageof relational structures
and Boolean algebras, GAdel's completeness theorem, models of Peano
arithmetic, and much more.
Part II focuses on a number of advanced theorems that are central
to the field, such as GAdel's first and second theorems of
incompleteness, the independence proof of Goodstein's theorem from
Peano arithmetic, Tarski's theorem on real closed fields, and
others. No other text contains complete and precise proofs of all
of these theorems.
With a solid and comprehensive program of exercises and selected
solution hints, Logic of Mathematics is ideal for classroom use-the
perfect textbook for advanced students of mathematics, computer
science, and logic.
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