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After Gödel. (English) Zbl 1111.03002
A sampler of results that, in one way or another, have roots in Gödel’s work. There are brief discussions of nonstandard models and of Hilbert’s Tenth Problem and Diophantine equations. The paper also sketches a model-theoretic proof, due to Kripke, of the existence of undecidable sentences. (H. Putnam has provided a fuller exposition of Kripke’s proof in [Notre Dame J. Formal Logic 41, No. 1, 53–58 (2000; Zbl 1005.03054)]). Finally, the paper presents a new application of Gödelian arguments to scientific epistemology.

MSC:
03-03 History of mathematical logic and foundations
03-02 Research exposition (monographs, survey articles) pertaining to mathematical logic and foundations
03A05 Philosophical and critical aspects of logic and foundations
03C62 Models of arithmetic and set theory
03H15 Nonstandard models of arithmetic
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