In the literature one can find three quite different proofs of the completeness of the infinite-valued sentential calculus of Lukasiewicz [8]: (i). the syntactical proof of Rose and Rosser [7], using McNaughton’s theorem, (ii). the algebraic proof of Chang [1, 2], using quantifier elimination in the first-order theory of divisible totally ordered abelian groups, and (iii). the recent proof of Cignoli [3], using the representation of free lattice ordered abelian groups.
A PROOF OF THE COMPLETENESS OF THE INFINITE-VALUED CALCULUS OF LUKASIEWICZ WITH ONE VARIABLE / D. MUNDICI; M. PASQUETTO. - STAMPA. - (1995), pp. 107-123. [10.1007/978-94-011-0215-5_6]
A PROOF OF THE COMPLETENESS OF THE INFINITE-VALUED CALCULUS OF LUKASIEWICZ WITH ONE VARIABLE
MUNDICI, DANIELE;
1995
Abstract
In the literature one can find three quite different proofs of the completeness of the infinite-valued sentential calculus of Lukasiewicz [8]: (i). the syntactical proof of Rose and Rosser [7], using McNaughton’s theorem, (ii). the algebraic proof of Chang [1, 2], using quantifier elimination in the first-order theory of divisible totally ordered abelian groups, and (iii). the recent proof of Cignoli [3], using the representation of free lattice ordered abelian groups.
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