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Completeness and interpolation of almost-everywhere quantification over finitely additive measures

Authors

  • João Rasga,

    1. Departamento de Matemática, Instituto Superior Técnico, Universidade de Lisboa, Avenida Rovisco Pais, Lisboa, Portugal
    2. Security and Quantum Information Group, Instituto de Telecomunicações, Avenida Rovisco Pais, Lisboa, Portugal
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  • Wafik Boulos Lotfallah,

    1. Department of Mathematics and Actuarial Science, American University in Cairo, New Cairo, Egypt
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  • Cristina Sernadas

    1. Departamento de Matemática, Instituto Superior Técnico, Universidade de Lisboa, Avenida Rovisco Pais, Lisboa, Portugal
    2. Security and Quantum Information Group, Instituto de Telecomunicações, Avenida Rovisco Pais, Lisboa, Portugal
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Abstract

We give an axiomatization of first-order logic enriched with the almost-everywhere quantifier over finitely additive measures. Using an adapted version of the consistency property adequate for dealing with this generalized quantifier, we show that such a logic is both strongly complete and enjoys Craig interpolation, relying on a (countable) model existence theorem. We also discuss possible extensions of these results to the almost-everywhere quantifier over countably additive measures.

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