We revisit the foundations of positive model theory, introducing h-inductive sentences. These allow a considerably simplified presentation of positive model theory, as well as a characterisation of Hausdorff cats by an amalgamation property of their h-inductive theory.

We revisit the foundations of positive model theory, introducing h-inductive sentences. These allow a considerably simplified presentation of positive model theory, as well as a characterisation of Hausdorff cats by an amalgamation property of their h-inductive theory.

La Logique positive a été introduite au début de ce troisième millénaire par Itaï Ben Yaacov, qui y a été conduit par une nécessité interne à la Théorie des modèles. Dans ce contexte de validité du Théorème de compacité, l’absence de négation provoque des situations inhabituelles, comme celle des structures infinies qui ont une extension élémentaire maximale, que nous étudions ici.

We continue [2], developing simplicity in the framework of compact abstract theories. Due to the generality of the context we need to introduce definitions which differ somewhat from the ones use in first order theories. With these modified tools we obtain more or less classical behaviour: simplicity is characterized by the existence of a certain notion of independence, stability is characterized by simplicity and bounded multiplicity, and hyperimaginary canonical bases exist.

We define elementary extension and elementary equivalence in Positive Logic.