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

Studia Logica 38 (1):49 - 73 (1979)
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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Marcel Crabbé (1999). The 3-Stratifiable Theorems of $\Mathit{NFU}_\Infty$. Notre Dame Journal of Formal Logic 40 (2):174-182.

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