Modèles saturés et modèles engendrés par des indiscernables

Publisher： Cambridge University Press

E-ISSN： 1943-5886|66|1|325-348

ISSN： 0022-4812

Source： The Journal of Symbolic Logic, Vol.66, Iss.1, 2001-03, pp. : 325-348

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Abstract

In the early eighties, answering a question of A. Macintyre, J. H. Schmerl ([13]) proved that every countable recursively saturated structure, equipped with a function β encoding the finite functions, is the β-closure of an infinite indiscernible sequence. This result implies that every countably saturated structure, in a countable but not necessarily recursive language, is an Ehrenfeucht-Mostowski model, by which we mean that the structure expands, in a countable language, to the Skolem hull of an infinite indiscernible sequence (in the new language).

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