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Finite-Variable Logics Do Not Have Weak Beth Definability Property

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The Road to Universal Logic

Part of the book series: Studies in Universal Logic ((SUL))

Abstract

We prove that n-variable logics do not have the weak Beth definability property, for all \(n\geq 3\). This was known for n = 3 (Ildikó Sain and András Simon), and for \(n\geq 5\) (Ian Hodkinson). Neither of the previous proofs works for n = 4. In this paper, we settle the case of n = 4, and we give a uniform, simpler proof for all \(n\geq 3\). The case for n = 2 is left open.

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Acknowledgment

This work was completed with the support of Hungarian National Grant for Basic Research No 81188.

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Authors and Affiliations

  1. MTA Alfréd Rényi Institute of Mathematics, Hungarian Academy of Sciences, Budapest, Hungary

    Hajnal Andréka & István Németi

Authors
  1. Hajnal Andréka
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  2. István Németi
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Correspondence to Hajnal Andréka .

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Editors and Affiliations

  1. City University of New York, New York, New York, USA

    Arnold Koslow

  2. Federal University of Santa Catarina, Florianópolis, Santa Catarina, Brazil

    Arthur Buchsbaum

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Andréka, H., Németi, I. (2015). Finite-Variable Logics Do Not Have Weak Beth Definability Property. In: Koslow, A., Buchsbaum, A. (eds) The Road to Universal Logic. Studies in Universal Logic. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-15368-1_4

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