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arXiv · 1607.03068

Metric logical categories and conceptual completeness for first order continuous logic

Jean-Martin Albert·Bradd Hart
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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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Jean-Martin Albert, Bradd Hart. 2016-07-11. Metric logical categories and conceptual completeness for first order continuous logic. https://arxiv.org/abs/1607.03068

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