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A Game-Based Formal System for Ł${}_{\infty}$

Alan Adamson and Robin Giles
Studia Logica: An International Journal for Symbolic Logic
Vol. 38, No. 1 (1979), pp. 49-73
Published by: Springer
Stable URL: http://www.jstor.org/stable/20014928
Page Count: 25
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A Game-Based Formal System for Ł${}_{\infty}$
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Abstract

A formal system for Ł${}_{\infty}$, based on a "game-theoretic" analysis of the Łukasiewicz propositional connectives, is defined and proved to be complete. An "Herbrand theorem" for the Ł${}_{\infty}$ predicate calculus (a variant of some work of Mostowski) and some corollaries relating to its axiomatizability are proved. The predicate calculus with equality is also considered.

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