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Mathematical Logic (Dover Books on Mathematics)

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After the appearance in 1952 of my "Introduction to Metamathematics", written for students at the first-year graduate level, I had no expectation of writing another text. But various occasions arose which required me to think about how to present parts of the same material more briefly, to a more general audience, or to students at an earlier educational level.* These newer expositions were received well enough that 1 was persuaded to prepare the present book for undergraduate students in the Junior year. In "Introduction to Metamathematics", the study of mathematical logic begins properly only in Chapter V (with some definitions in Chapter IV). Graduate students in mathematics can cover rapidly the introductory material which precedes it there. But for less advanced students or in shorter courses, too much time would be used by such a thorough intro- duction. I am now convinced that it is also sound pedagogically and scientifically to start doing logic (correctly) right from the beginning, even if not all the reasons for doing it nor all the criteria governing how it is done have been enumerated in advance. The rest of the "introduction" can come later.


Undergraduate students with no prior instruction in mathematical logic will benefit from this multi-part text. Part I offers an elementary but thorough overview of mathematical logic of 1st order. Part II introduces some of the newer ideas and the more profound results of logical research in the 20th century. 1967 edition.
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