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Non-standard Stochastics with a First Order Algebraization

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Abstract

Internal sets and the Boolean algebras of the collection of the internal sets are of central importance in non-standard analysis. Boolean algebras are the algebraization of propositional logic while the logic applied in non-standard analysis (in non-standard stochastics) is the first order or the higher order logic (type theory). We present here a first order logic algebraization for the collection of internal sets rather than the Boolean one. Further, we define an unusual probability on this algebraization.

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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. Non-standard Stochastics with a First Order Algebraization. Stud Logica 95, 345–354 (2010). https://doi.org/10.1007/s11225-010-9266-2

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  • DOI: https://doi.org/10.1007/s11225-010-9266-2

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