n-dependent continuous theories and hyperdefinable sets

Adrián Portillo Fernández

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arXiv · 2405.19830

n-dependent continuous theories and hyperdefinable sets

Adrián Portillo Fernández

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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.

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BibTeX RIS

Adrián Portillo Fernández. 2024-05-30. n-dependent continuous theories and hyperdefinable sets. https://arxiv.org/abs/2405.19830

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