Submission date: 4 June 2015.

Abstract:

This paper is a general and elementary introduction to Positive Logic, where only the said h-inductive sentences are under consideration, allowing the extension to homomorphisms of model-theoric notions which are classically associated to embeddings, in particular the notion of existentially closed models primitively defined by Abraham Robinson, which become here positively closed models. It differs from the exposition paper of Ben Yaacov and Poizat 2007, that it summarizes sometimes, because it is more concise, because it accounts for recent results in this domain, and because it is oriented towards the positivisation of Jonsson theories. It contains in its appendix some practical tools for the determination of the h-inductive theory of a given structure, in a concrete context.

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