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A constructive proof of McNaughton’s theorem in infinite-valued logic. (English) Zbl 0807.03012

A constructive proof is given of K. McNaughton’s theorem [J. Symb. Log. 16, 1-13 (1951; Zbl 0043.009)] stating that every piecewise linear function with integral coefficients is representable by some sentence in the infinite-valued calculus of Łukasiewicz. The proof uses Minkowski’s convex body theorem and the Turing machine is described that effectively computes a disjunction of sentences that represents that function.
Reviewer: A.Hoogewijs (Gent)

MSC:

03B50 Many-valued logic
03F60 Constructive and recursive analysis
03D10 Turing machines and related notions

Citations:

Zbl 0043.009
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References:

[1] Introduction to piecewise-linear topology (1972)
[2] DOI: 10.1090/S0002-9947-1958-0094299-1 · doi:10.1090/S0002-9947-1958-0094299-1
[3] A theorem about infinite-valued sentential logic 16 pp 1– (1951) · Zbl 0043.00901
[4] Logic, semantics, metamathematics pp 38– (1956)
[5] Grundlagen der Mathematischen Wissenschaften 99 (1959)
[6] Lattice-ordered groups, An introduction (1988) · Zbl 0636.06008
[7] Piecewise linear topology (1968)
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