### Generalized effective completeness for continuous logic

#### Abstract

In this paper, we present a generalized effective completeness theorem for continuous logic. The primary result is that any continuous theory is satisfied in a structure which admits a presentation of the same Turing degree. It then follows that any decidable theory is satisfied by a computably presentable structure. This modifies and extends previous partial effective completeness theorems for continuous logic given by Calvert and Didehvar, Ghasemloo, and Pourmahdian.

#### Keywords

Effective completeness; Continuous logic; Metric structures; Computable presentations

#### Full Text:

4. [PDF]DOI: https://doi.org/10.4115/jla.2023.15.4

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Journal of Logic and Analysis ISSN: 1759-9008