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On the scope of the classical deduction theorem

Published online by Cambridge University Press:  12 March 2014

Witold A. Pogorzelski
Witold A. Pogorzelski*
Affiliation:
University of Wroclaw, Poland
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Extract

§1. The set Cn(R, A + X) is the set of all expressions deducible, on the ground of formulas A, from the class X of formulas of the implicational propositional calculus, by means of rules belonging to the set R. In other words, Cn(R, A + X) is the set of expressions obtained from the set X by the help of a two-parameter function Cn[R, A]. The formula is called the classical deduction theorem.

The classical deduction theorem is true for the system 〈R, A〉 (where R is the set of primitive rules, A is the set of axioms of the propositional calculus) if it holds for the function Cn[R, A].

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 33 , Issue 1 , 26 April 1968 , pp. 77 - 81
Copyright
Copyright © Association for Symbolic Logic 1968

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References

[1]Hilbert, D. and Bernays, P., Grundlagen der Mathematik, Band II, Supplement III, Springer, Berlin, 1939.Google Scholar
[2]Łoś, J. and Suszko, R., Remarks on sentential logics, Koninklijke Nederlandse Akademie van Wetenschappen. Proceedings. Series A. Mathematical Sciences, vol. 61 (1938).Google Scholar
[3]Tarski, A., Fandamentale Begriffe der Methodologie der deduktiven Wissenschaften Monatshefte für Mathematik und Physik, XXXVII Bd, 1930.Google Scholar