A Model Theory for the Potential Infinite
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RIS BIB ENDNOTEA Model Theory for the Potential Infinite
Publication date: 28.11.2022
Reports on Mathematical Logic, 2022, Number 57, pp. 3-30
https://doi.org/10.4467/20842589RM.22.001.16658Authors
A Model Theory for the Potential Infinite
We present the model theoretic concepts that allow mathematics to be developed with the notion of the potential infinite instead of the actual infinite. The potential infinite is understood as a dynamic notion, being an indefinitely extensible finite. The main adoption is the interpretation of the universal quantifier, which has an implicit reection principle. Each universal quantification refers to an indefinitely large, but finite set. The quantified sets may increase, so after a reference by quantification, a further reference typically uses a larger, still finite set. We present the concepts for classical first-order logic and show that these dynamic models are sound and complete with respect to the usual inference rules. Moreover, a finite set of formulas requires a finite part of the increasing model for a correct interpretation.
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Information: Reports on Mathematical Logic, 2022, Number 57, pp. 3-30
Article type: Original article
Mathematisches Institut, LMU, Theresienstr. 39, D-80333 München, Germany
Published at: 28.11.2022
Received at: 04.05.2021
Article status: Open
Licence: CC BY
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English