A model theory for the potential infinite

• Autorzy: Eberl Matthias

Identyfikatory

DOI

10.4467/20842589RM.22.001.16658

• Języki publikacji: EN

Abstrakty

EN

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 reflection 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.

Słowa kluczowe

EN

finitism; potential infinite; model theory; first-order logic; reflection principle

• Wydawca: Wydawnictwo Uniwersytetu Jagiellońskiego
• Czasopismo: Reports on Mathematical Logic
• Rocznik: 2022
• Tom: Vol. 57
• Strony: 3--29
• Opis fizyczny: Bibliogr. 12 poz.

Twórcy

autor

Eberl Matthias

• Mathematisches Institut, LMU, Theresienstr. 39, D-80333 M¨unchen, Germany

Bibliografia

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Uwagi

Opracowanie rekordu ze środków MEiN, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2022-2023).