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Other Proofs of Old Results
Author(s) -
Kotlarski Henryk
Publication year - 1998
Publication title -
mathematical logic quarterly
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.473
H-Index - 28
eISSN - 1521-3870
pISSN - 0942-5616
DOI - 10.1002/malq.19980440406
Subject(s) - mathematical proof , lemma (botany) , mathematics , gödel's completeness theorem , completeness (order theory) , proofs of fermat's little theorem , arithmetic function , discrete mathematics , calculus (dental) , analytic proof , algebra over a field , fundamental theorem , pure mathematics , compactness theorem , fixed point theorem , mathematical analysis , medicine , ecology , geometry , poaceae , dentistry , biology
Abstract We transform the proof of the second incompleteness theorem given in [3] to a proof‐theoretic version, avoiding the use of the arithmetized completeness theorem. We give also new proofs of old results: The Arithmetical Hierarchy Theorem and Tarski's Theorem on undefinability of truth; the proofs in which the construction of a sentence by means of diagonalization lemma is not needed.