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Mathematics | A Course on Mathematical Logic

A Course on Mathematical Logic

Series: Universitext

Srivastava, Shashi Mohan

2008

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  • Written in a clear, concise style
  • Contains numerous exercises and examples
  • Employs Godel’s completeness and incompleteness theorems to motivate the entire text
  • Uses modern language and notation, which will appeal to undergrads as well as graduate students

This is a short, distinctive, modern, and motivated introduction to mathematical logic for senior undergraduate and beginning graduate students in mathematics and computer science. Any mathematician who is interested in knowing what logic is concerned with and who would like to learn Gödel’s incompleteness theorems should find this book particularly convenient. The treatment is thoroughly mathematical, and the entire subject has been approached like a branch of mathematics. Serious efforts have been made to make the book suitable for the classroom as well as for self-reading. The book does not strive to be a comprehensive encyclopedia of logic. Still, it gives essentially all the basic concepts and results in mathematical logic. The book prepares students to branch out in several areas of mathematics related to foundations and computability such as logic, axiomatic set theory, model theory, recursion theory, and computability. The main prerequisite for this book is the willingness to work at a reasonable level of mathematical rigor and generality.

Shashi Mohan Srivastava is a Professor at the Indian Statistical Institute, Kolkata, India. He is also the author of A Course on Borel Sets, GTM 180.

Content Level » Research

Keywords » computability theory - mathematical logic - model theory - proof - set theory

Related subjects » Algebra - Mathematics

Table of contents 

Syntax of First-Order Logic.- Semantics of First-Order Languages.- Propositional Logic.- Proof and Metatheorems in First-Order Logic.- Completeness Theorem and Model Theory.- Recursive Functions and Arithmetization of Theories.- Incompleteness Theorems and Recursion Theory.

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