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On complexity reduction of Σ1 formulas

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Abstract.

 For a fixed q  ℕ and a given Σ1 definition φ(d,x), where d is a parameter, we construct a model M of 1 Δ0 + ¬ exp and a non standard d  M such that in M either φ has no witness smaller than d or phgr; is equivalent to a formula ϕ(d,x) having no more than q alternations of blocks of quantifiers.

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Authors and Affiliations

  1. Math. Institute of the Polish Academy of Sciences, Sniadeckich 8, 00-950 Warszawa, Poland. e-mail: zosiaa@panim.impan.gov.pl, , , , , , PL

    Zofia Adamowicz

  2. Dept. of Math. Warsaw University, Banacha 2, Warszawa, Poland (died on 6. 03. 2002), , , , , , PL

    Pawe Zbierski

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  1. Zofia Adamowicz
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  2. Pawe Zbierski
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Received: 29 September 1998 / Revised version: 7 November 2001 Published online: 10 October 2002

RID="⋆"

ID="⋆" Research supported in part by The State Committee for Scientific Research (Poland), KBN, grant number 2 PO3A 018 13.

RID="⋆"

ID="⋆" Research supported in part by The State Committee for Scientific Research (Poland), KBN, grant number 2 PO3A 018 13.

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Adamowicz, Z., Zbierski, P. On complexity reduction of Σ1 formulas. Arch. Math. Logic 42, 45–58 (2003). https://doi.org/10.1007/s001530200145

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  • DOI: https://doi.org/10.1007/s001530200145

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