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Books : reviews

J. N. Crossley, C. J. Ash, C. J. Brickhill, John C. Stillwell, N. H. Williams.
What is Mathematical Logic?.
OUP. 1972

This stimulating introduction draws together in a readable form the major issues and recent developments of modern mathematical logic. Gödel’s theorems, computability and recursive functions, and consistency and independence in axiomatic set theory, are all clearly explained. Both the non-logician and the reader embarking on serious study of the subject will find this book invaluable.

John C. Stillwell.
Roads to Infinity: the mathematics of truth and proof.
CRC Press. 2010

John C. Stillwell.
Reverse Mathematics: proofs from the inside out.
Princeton University Press. 2018

The first book surveying the history and ideas behind reverse mathematics

Reverse mathematics is a new field that seeks to find the axioms needed to prove given theorems. In Reverse Mathematics, John Stillwell offers a historical and representative view, emphasizing basic analysis and giving a novel approach to logic. By using a minimum of mathematical logic in a well-motivated way, Reverse Mathematics will engage advanced undergraduates and all mathematicians interested in the foundations of mathematics.