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Formal methods. An introduction to symbolic logic and to the study of effective operations in arithmetic and logic. (English) Zbl 0105.24503

Synthese Library. Dordrecht-Holland: D. Reidel Publishing Company. xiv, 170 p. (1962).
This is an introduction to modern mathematical logic differing in several respects from the current ones. The author explains the different treatments of mathematical logic, their connection and respective merits. The author’s techniques of semantic and deductive tableaux are given ample attention and elegant application. There is an account of syntactic and semantic incompleteness results, the theory of definition and a discussion of Craig’s interpolation theorem and Beth’s theorem on the independence of primitive notions.
The chapter-headings are: Purely implicational logic, Full sentential logic, Theory of quantification, equality and functionality, Completeness of elementary logic, The formalization of arithmetic and its limitations, The theory of definition, On machines which prove theorems; Appendix: supplementary explanations.

MSC:

03-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to mathematical logic and foundations