Mundici, Daniele A constructive proof of McNaughton’s theorem in infinite-valued logic. (English) Zbl 0807.03012 J. Symb. Log. 59, No. 2, 596-602 (1994). 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) Cited in 1 ReviewCited in 38 Documents MSC: 03B50 Many-valued logic 03F60 Constructive and recursive analysis 03D10 Turing machines and related notions Keywords:piecewise linear function; infinite-valued calculus of Łukasiewicz; Minkowski’s convex body theorem Citations:Zbl 0043.009 PDFBibTeX XMLCite \textit{D. Mundici}, J. Symb. Log. 59, No. 2, 596--602 (1994; Zbl 0807.03012) Full Text: DOI 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) This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.