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First-order spectra with one binary predicate

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Book cover Computer Science Logic (CSL 1994)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 933))

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Abstract

The spectrum, Sp(ϕ), of a sentence ϕ is the set of cardinalities of finite structures which satisfy ϕ. We prove that any set of integers which is in Func ∞1 i.e. in the class of spectra of first-order sentences of type containing only unary function symbols is also in BIN 1 i.e. in the class of spectra of first-order sentences of type involving only a single binary relation.

We give similar results for generalized spectra and some corollaries: in particular, from the fact that the large complexity class \(\mathop \cup \limits_c \) NTIME RAM (cn) is included in Func ∞1 for unary languages (n denotes the input integer), we deduce that the set of primes and many “natural” sets belong to BIN 1

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Authors and Affiliations

  1. LAIAC, Université de Caen, France

    Arnaud Durand & Solomampionona Ranaivoson

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  1. Arnaud Durand
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  2. Solomampionona Ranaivoson
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Leszek Pacholski Jerzy Tiuryn

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© 1995 Springer-Verlag Berlin Heidelberg

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Durand, A., Ranaivoson, S. (1995). First-order spectra with one binary predicate. In: Pacholski, L., Tiuryn, J. (eds) Computer Science Logic. CSL 1994. Lecture Notes in Computer Science, vol 933. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0022255

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  • DOI: https://doi.org/10.1007/BFb0022255

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-60017-6

  • Online ISBN: 978-3-540-49404-1

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