Cover image for The foundations of mathematics in the theory of sets
Title:
The foundations of mathematics in the theory of sets
Personal Author:
Series:
Encyclopedia of mathematics and its applications ; v.82
Publication Information:
Cambridge, U.K. : Cambridge University Press, 2000
ISBN:
9780521770347
Subject Term:

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30000004823518 QA248 M39 2000 Open Access Book Book
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Summary

Summary

This 2001 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'. This leads to an investigation of the logic of quantification over the universe of sets and a discussion of its role in second order logic, as well as in the analysis of proof by induction and definition by recursion. The subject matter of the book falls on the borderline between philosophy and mathematics, and should appeal to both philosophers and mathematicians with an interest in the foundations of mathematics.