Customer Reviews

A Tour Through Mathematical Logic (Carus Mathematical Monographs)

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This tour is both broad and deep; it covers most of what would ordinarily be considered upper level material in the foundations of mathematics. While it contains theorems, proofs and exercises, it does not have the structure of a textbook. It is more on the order of an advanced survey that includes history. There are occasional short sections reserved for biographies of mathematicians of note in the field. For example, there are biographies of Bertrand Russell, Euclid, Georg Cantor, John von Neumann and Julia Robinson.

The chapter headings are:

*) Predicate logic

*) Axiomatic set theory

*) Recursion theory and computability

*) Godel's incompleteness theorems

*) Model theory

*) Contemporary set theory

*) Nonstandard analysis

*) Constructive mathematics

Given the branching away from logic into set theory and analysis, in my opinion, this book is best considered a survey of the foundations of mathematics. Considered in that way, it is a sound primer for people with mathematical maturity. If you have an interest in advanced material in these areas, you will find this book worthy of study.