Metric logical categories and conceptual completeness for first order continuous logic

2016/07/11 by Albert, Jean-Martin, Hart, Bradd
#FOS: Mathematics #Logic (math.LO)

paper · doi:10.48550/arxiv.1607.03068

Abstract

We begin the study of categorical logic for continuous model theory. In particular, we 1. introduce the notions of metric logical categories and functors as categorical equivalents of a metric theory and interpretations, 2. prove a continuous version of conceptual completeness showing that T^\eq is the maximal conservative expansion of T, and 3. define the concept of a metric pre-topos.

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