Maximal Logics

descriptionPublicationkeyboard_double_arrow_right Article 01 Apr 1977Publisher:JSTORJournal:Proceedings of the American Mathematical Society, volume 63, page 291 (issn: 0002-9939,

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Authors: Sgro, Joseph;

doi: 10.2307/2041807 , 10.1090/s0002-9939-1977-0491143-2

Maximal Logics

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Abstract

In this paper we present a general method for producing logics on various classes of models which are maximal with respect to a Łoś ultraproducts theorem. As a corollary we show that L Top {\mathcal {L}^{{\text {Top}}}} is maximal. We also show that these maximal logics satisfy the Souslin-Kleene property.

Keywords

definability, ultraproduct, category theoretical methods, Ultraproducts and related constructions, Abstract model theory, Special categories, abstract model theory, invariant logic

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