Forcing for First-Order Languages from the Perspective of Rasiowa-Sikorski Lemma

• Autorzy: Czelakowski J.

Identyfikatory

DOI

10.3233/FI-2017-1608

• Języki publikacji: EN

Abstrakty

EN

The paper is concerned with the problem of building models for first-order languages from the perspective of the classic paper of Rasiowa and Sikorski [9]. The central idea, developed in this paper, consists in constructing first-order models from individual variables. The key notion of a Rasiowa–Sikorski set of formulas for an arbitrary countable language L is examined. Each Rasiowa–Sikorski set defines a countable model for L. Conversely, every countable model for L is determined by a Rasiowa-Sikorski set. The focus is on constructing Rasiowa-Sikorski sets by applying forcing techniques restricted to Boolean algebras arising from the subsets of the set of atomic formulas of L.

Słowa kluczowe

EN

first-order logic; substitutional semantics; Lindenbaum set; Rasiowa–Sikorski set; Boolean algebra; ultrafilter; forcing

• Wydawca: IOS Press
• Czasopismo: Fundamenta Informaticae
• Rocznik: 2017
• Tom: Vol. 156, nr 3/4
• Strony: 255--280
• Opis fizyczny: Bibliogr. 15 poz.

Twórcy

autor

Czelakowski J.

• Insitute of Mathematics and Informatics, Opole University, Opole, Poland

Bibliografia

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Uwagi

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