On perturbations of continuous structures

Details On perturbations of continuous structures On perturbations of continuous structures

2008-02-29

arxiv.org/abs/0802.4388v2

Journal of Mathematical Logic 8, 2 (2008) 225-249

Mathematics

Logic

Scientific paper

10.1142/S0219061308000762

We give a general framework for the treatment of perturbations of types and structures in continuous logic, allowing to specify which parts of the logic may be perturbed. We prove that separable, elementarily equivalent structures which are approximately $\aleph_0$-saturated up to arbitrarily small perturbations are isomorphic up to arbitrarily small perturbations (where the notion of perturbation is part of the data). As a corollary, we obtain a Ryll-Nardzewski style characterisation of complete theories all of whose separable models are isomorphic up to arbitrarily small perturbations.

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