n-dependent continuous theories and hyperdefinable sets

TL;DR

This paper introduces the continuous modeling property for structures, linking it to the embedding Ramsey property, and uses indiscernible sequences to characterize n-dependence in continuous theories and hyperdefinable sets.

Contribution

It establishes a new equivalence between the continuous modeling property and the embedding Ramsey property, and characterizes n-dependence via indiscernible sequences in continuous logic.

Findings

Continuous modeling property is equivalent to the embedding Ramsey property.

Generalized indiscernible sequences characterize n-dependence in continuous theories.

Provides a framework for analyzing hyperdefinable sets in continuous logic.

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.