Grigori Mints Thoralf Skolem and the Epsilon Substitution Method for Predicate Logic *
نویسندگان
چکیده
Skolem’s contributions to mathematical logic are fundamental and far-reaching. A good survey by Hao Wang (1970) is presented in Fenstad’s collection of Skolem’s works (1970). Even Skolemization, i.e. the replacement of quantifiers by new constant and function symbols, is too extensive for one talk. Cf. my survey (Mints 1990) of proof-theoretic aspects and more recent work (Shankar 1992) concerning dynamic Skolemization in automated deduction. Here I relate some of Skolem’s work (Skolem 1929, §5) to the substitution method, which was the center of interest of Hilbert’s school in 1920–1930. Hao Wang (1970, p. 26) says: “It is hard to evaluate the importance of the proofs and comments in this section”. I show that constructions in Skolem 1929, §5 can be seen as instances of the substitution method and the proof of -theorems. They provide speedup estimates. I review this material in section 2 and then describe some of the later developments taking models (solutions in Skolem’s terminology) into account.
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