There is No Standard Model of ZFC and ZFC2

Foukzon, Jaykov and Men'kova, Elena (2018) There is No Standard Model of ZFC and ZFC2. Journal of Advances in Mathematics and Computer Science, 26 (2). pp. 1-20. ISSN 24569968

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Abstract

In this paper we view the rst order set theory ZFC under the canonical rst order semantics and the second order set theory ZFC2 under the Henkin semantics. Main results are: (i) Let MZFCst be a standard model of ZFC, then ¬Con(ZFC +∃MZFCst ).
(ii) Let MZFC2st be a standard model of ZFC2 with Henkin semantics, then ¬Con(ZFC2 +∃MZFC2st ).
(iii) Let k be inaccessible cardinal then ¬Con(ZFC + ∃κ).In order to obtain the statements (i) and (ii) examples of the inconsistent countable set in a settheory ZFC + ∃MZFCst and in a set theory ZFC2 + ∃MZFC2st were derived.
It is widely believed that ZFC + ∃MZFCst and ZFC2 + ∃MZFC2st are inconsistent, i.e. ZFC andZFC2 have a standard models. Unfortunately this belief is wrong.

Item Type: Article
Subjects: Eprints AP open Archive > Mathematical Science
Depositing User: Unnamed user with email admin@eprints.apopenarchive.com
Date Deposited: 25 Apr 2023 11:08
Last Modified: 05 Feb 2024 04:50
URI: http://asian.go4sending.com/id/eprint/217

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