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On Conservative Extensions in Logics with Infinitary Predicates

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Abstract

If the language is extended by new individual variables, in classical first order logic, then the deduction system obtained is a conservative extension of the original one. This fails to be true for the logics with infinitary predicates. But it is shown that restricting the commutativity of quantifiers and the equality axioms in the extended system and supposing the merry-go-round property in the original system, the foregoing extension is already conservative. It is shown that these restrictions are crucial for an extension to be conservative. The origin of the results is algebraic logic.

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Authors and Affiliations

  1. Department of Algebra, Budapest University of Technology and Economics, H–1521, Budapest, Hungary

    Miklós Ferenczi

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  1. Miklós Ferenczi
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Correspondence to Miklós Ferenczi.

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Supported by grant OTKA T43242.

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Ferenczi, M. On Conservative Extensions in Logics with Infinitary Predicates. Stud Logica 92, 121–135 (2009). https://doi.org/10.1007/s11225-009-9189-y

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  • DOI: https://doi.org/10.1007/s11225-009-9189-y

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