Unifying some notions of infinity in ZC and ZF

• Autorzy: Oman G.

Identyfikatory

DOI

10.4467/20842589RM.16.004.5281

• Języki publikacji: EN

Abstrakty

EN

Let ZC - I (respectively, ZF - Ί ) be the theory obtained by deleting the axiom of infinity from the usual list of axioms for Zermelo set theory with choice (respectively, the usual list of axioms for Zermelo-Fraenkel set theory). In this note, we present a collection of sentences φ() for which (ZC - Ί) + φ() (respectively, (ZF - Ί)+φ()) proves the existence of an infinite set.

Słowa kluczowe

EN

Dedekind-infinite set; Peano system; Tarski-infinite set; Zermelo-Fraenkel set theory; Zermelo set theory with choice

• Wydawca: Wydawnictwo Uniwersytetu Jagiellońskiego
• Czasopismo: Reports on Mathematical Logic
• Rocznik: 2016
• Tom: Vol. 51
• Strony: 43--56
• Opis fizyczny: Bibliogr. 26 poz.

Twórcy

autor

Oman G.

• Department of Mathematics The University of Colorado Colorado Springs, CO 80918 USA

Bibliografia

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Uwagi

PL

Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę.