Yet another proof of Goedel's completeness theorem for first-order classical logic

Details Yet another proof of Goedel's completeness theorem for first-order classical logic Yet another proof of Goedel's completeness theorem for first-order classical logic

2009-10-11

arxiv.org/abs/0910.2059v1

Mathematics

Logic

21 pages

Scientific paper

A Henkin-style proof of completeness of first-order classical logic is given with respect to a very small set (notably missing cut rule) of Genzten deduction rules for intuitionistic sequents. Insisting on sparing on derivation rules, satisfiability theorem is seen to need weaker assumptions than completeness theorem, the missing request being exactly the rule ~ p --> p, which gives a hint of intuitionism's motivations from a classical point of view. A bare treatment of standard, basic first-order syntax somehow more algebraic-flavoured than usual is also given.

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