Positive Jonsson Theories

Abstract

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.

Résumé

Cet article est une introduction générale à la Logique Positive, où seuls sont considérés les énoncés dits h-inductifs, ce qui permet d’étendre aux homomorphismes les notions de Théorie des Modèles classiquement associées aux plongements; en particulier les modèles existentiellement clos, primitivement définis par Abraham Robinson, deviennent ici les modèles positivement clos. Il tient compte de résultats récents en ce domaine, et se focalise sur ce que deviennent les théories de Jonsson dans un contexte positif.

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Correspondence to Bruno Poizat.

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This paper is dedicated to the memory of Tölendi Garifuly.

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Poizat, B., Yeshkeyev, A. Positive Jonsson Theories. Log. Univers. 12, 101–127 (2018). https://doi.org/10.1007/s11787-018-0185-8

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Keywords

  • Model theory
  • inductive limit
  • compactness
  • Jonsson theory
  • amalgams

Mathematics Subject Classification

  • 03C07
  • 03C10
  • 03C52