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Quelques effets pervers de la positivité

Annals of Pure and Applied Logic 161 (6):812-816 (2010)

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Positive Model Theory and Amalgamations.Mohammed Belkasmi - 2014 - Notre Dame Journal of Formal Logic 55 (2):205-230.details We continue the analysis of foundations of positive model theory as introduced by Ben Yaacov and Poizat. The objects of this analysis are $h$-inductive theories and their models, especially the “positively” existentially closed ones. We analyze topological properties of spaces of types, introduce forms of quantifier elimination, and characterize minimal completions of arbitrary $h$-inductive theories. The main technical tools consist of various forms of amalgamations in special classes of structures. Download Export citation Bookmark 6 citations
Positive Jonsson Theories.Bruno Poizat & Aibat Yeshkeyev - 2018 - Logica Universalis 12 (1-2):101-127.details This paper is a general introduction to Positive Logic, where only what we call h-inductive sentences are under consideration, allowing the extension to homomorphisms of model-theoric notions which are classically associated to embeddings; in particular, the existentially closed models, that were primitively defined by Abraham Robinson, become here positively closed models. It accounts for recent results in this domain, and is oriented towards the positivisation of Jonsson theories. Download Export citation Bookmark 11 citations
Spaces of types in positive model theory.Levon Haykazyan - 2019 - Journal of Symbolic Logic 84 (2):833-848.details We introduce a notion of the space of types in positive model theory based on Stone duality for distributive lattices. We show that this space closely mirrors the Stone space of types in the full first-order model theory with negation (Tarskian model theory). We use this to generalise some classical results on countable models from the Tarskian setting to positive model theory. Download Export citation Bookmark 3 citations
Elementary Equivalence in Positive Logic Via Prime Products.Tommaso Moraschini, Johann J. Wannenburg & Kentaro Yamamoto - forthcoming - Journal of Symbolic Logic:1-18.details We introduce prime products as a generalization of ultraproducts for positive logic. Prime products are shown to satisfy a version of Łoś’s Theorem restricted to positive formulas, as well as the following variant of the Keisler Isomorphism Theorem: under the generalized continuum hypothesis, two models have the same positive theory if and only if they have isomorphic prime powers of ultrapowers. Download Export citation Bookmark

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