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The de Jongh property for Basic Arithmetic

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Abstract

We prove that Basic Arithmetic, BA, has the de Jongh property, i.e., for any propositional formula A(p 1,..., p n ) built up of atoms p 1,..., p n , BPC \({\vdash}\) A(p 1,..., p n ) if and only if for all arithmetical sentences B 1,..., B n , BA \({\vdash}\) A(B 1,..., B n ). The technique used in our proof can easily be applied to some known extensions of BA.

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Authors and Affiliations

  1. Department of Mathematical Sciences, Sharif University of Technology, Tehran, Iran

    Mohammad Ardeshir & S. Mojtaba Mojtahedi

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  1. Mohammad Ardeshir
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  2. S. Mojtaba Mojtahedi
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Correspondence to Mohammad Ardeshir.

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Ardeshir, M., Mojtahedi, S.M. The de Jongh property for Basic Arithmetic. Arch. Math. Logic 53, 881–895 (2014). https://doi.org/10.1007/s00153-014-0394-7

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  • DOI: https://doi.org/10.1007/s00153-014-0394-7

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