Structural logic and abstract elementary classes with intersections

• Autorzy: Boney Will , Vasey Sebastien

Identyfikatory

DOI

10.4064/ba8178-12-2018

• Języki publikacji: EN

Abstrakty

EN

We give a syntactic characterization of abstract elementary classes (AECs) closed under intersections using a new logic with a quantifier for isomorphism types that we call structural logic: we prove that AECs with intersections correspond to classes of models of a universal theory in structural logic. This generalizes Tarski’s syntactic characterization of universal classes. As a corollary, we prove that any AEC closed under intersections with countable Löwenheim-Skolem-Tarski number is axiomatizable in L_∞,ω(Q), where Q is the quantifier “there exist uncountably many”.

Słowa kluczowe

EN

abstract elementary classes; intersections; universal classes; structural logic

• Wydawca: Instytut Matematyczny PAN
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2019
• Tom: Vol. 67, no. 1
• Strony: 1--17
• Opis fizyczny: Bibliogr. 31 poz.

Twórcy

autor

Boney Will

• Department of Mathematics, Harvard University, Cambridge, MA 02138, U.S.A.

autor

Vasey Sebastien

• Department of Mathematics, Harvard University, Cambridge, MA 02138, U.S.A.

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Uwagi

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2019).