Submission date: 30 May 2024

Abstract:

We define the continuous modeling property for first-order structures and show that a first-order structure has the continuous modelling property if and only if its age has the embedding Ramsey property. We use generalized indiscernible sequences in continuous logic to study and characterize n-dependence for continuous theories and first-order hyperdefinable sets in terms of the collapse of indiscernible sequences.

Mathematics Subject Classification: 03C45

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Full text arXiv 2405.19830: pdf, ps.