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CONSTRUCTIVE REFLECTIVITY PRINCIPLES FOR REGULAR THEORIES
Stockholm University, Faculty of Science, Department of Mathematics.ORCID iD: 0000-0003-1390-2970
Number of Authors: 22019 (English)In: Journal of Symbolic Logic (JSL), ISSN 0022-4812, E-ISSN 1943-5886, Vol. 84, no 4, p. 1348-1367Article in journal (Refereed) Published
Abstract [en]

Classically, any structure for a signature may be completed to a model of a desired regular theory by means of the chase construction or small object argument. Moreover, this exhibits as weakly reflective in .

We investigate this in the constructive setting. The basic construction is unproblematic; however, it is no longer a weak reflection. Indeed, we show that various reflectivity principles for models of regular theories are equivalent to choice principles in the ambient set theory. However, the embedding of a structure into its chase-completion still satisfies a conservativity property, which suffices for applications such as the completeness of regular logic with respect to Tarski (i.e., set) models.

Unlike most constructive developments of predicate logic, we do not assume that equality between symbols in the signature is decidable. While in this setting, we also give a version of one classical lemma which is trivial over discrete signatures but more interesting here: the abstraction of constants in a proof to variables.

Place, publisher, year, edition, pages
2019. Vol. 84, no 4, p. 1348-1367
Keywords [en]
regular logic, constructive semantics, choice principles
National Category
Mathematics Computer and Information Sciences
Identifiers
URN: urn:nbn:se:su:diva-178716DOI: 10.1017/jsl.2019.70ISI: 000504566200003OAI: oai:DiVA.org:su-178716DiVA, id: diva2:1391586
Available from: 2020-02-05 Created: 2020-02-05 Last updated: 2020-02-06Bibliographically approved

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Lumsdaine, Peter Lefanu
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