The Proof of Certain Tarski's Theorem about the Existence of One-element Base for Axiomatizable Systems of Propositional Calculus

• Autorzy: Kaptur, M.
• Konferencja: X Polish-Czech Mathematical School (10 ; 04-07.06.2003 ; Poraj near Częstochowa, Poland)
• Języki publikacji: EN

Abstrakty

EN

In [1] the following theorem relating the existence of one-element base for spacious class of axiomatizable propositional calculus has been given: Theorem 1. System L, as well as each axiomatizable system propositional calculus, contains sentences "CpCqp" and „CpCqCCpCqrr" (or "CpCqCCpCqrCsr"), possesses the base consisting of only one sentence 1. In Postscript added to the English translation of publication [1] 2 the outline of proof of the above theorem, found by R. McKenzie, has been given. Author of the article advises to give the full proof of Theorem 1, because the outline contained in Postscript does not contain essential reasonings for the proof.

Słowa kluczowe

PL

twierdzenie Tarskiego; rachunek zdań

EN

Tarski's theorem; propositional calculus

• Czasopismo: Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
• Rocznik: 2003
• Tom: Vol. 9
• Strony: 51--59
• Opis fizyczny: Bibliogr. 3 poz.

Twórcy

autor

Kaptur, M.

• Institute of Mathematics and Computer Science, Pedagogical University of Częstochowa, Al. Armii Krajowej 13/15, 42-200 Częstochowa, Poland

Bibliografia

• [1] J. Łukasiewicz, A. Tarski, Untersuchungen über den Aussagenkalkül, Sprawozdania z Posiedzeń Towarzystwa Naukowego Warszawskiego, wyd. III, t. 23, s. 30-50, 1930.
• [2] A. Tarski, Logic, Semantics, Metamathematics, Papers from 1923 to 1938, Clarendon Press, Oxford, 1956, XIV+471 p.
• [3] A. Tarski, Pisma logiczno-filozoficzne, tom 2, Metalogika, (Tłumaczenie i redakcja Jan Zygmunt), PWN, Warszawa, 2001, XIV+516 s.