Notre Dame Journal of Formal Logic

Permutation Models and SVC

Eric J. Hall

Abstract

Let M be a model of ZFAC (ZFC modified to allow a set of atoms), and let N be an inner model with the same set of atoms and the same pure sets (sets with no atoms in their transitive closure) as M. We show that N is a permutation submodel of M if and only if N satisfies the principle SVC (Small Violations of Choice), a weak form of the axiom of choice which says that in some sense, all violations of choice are localized in a set. A special case is considered in which there exists an SVC witness which satisfies a certain homogeneity condition.

Article information

Source
Notre Dame J. Formal Logic, Volume 48, Number 2 (2007), 229-235.

Dates
First available in Project Euclid: 16 May 2007

Permanent link to this document
https://projecteuclid.org/euclid.ndjfl/1179323265

Digital Object Identifier
doi:10.1305/ndjfl/1179323265

Mathematical Reviews number (MathSciNet)
MR2306394

Zentralblatt MATH identifier
1201.03043

Subjects
Primary: 03E25: Axiom of choice and related propositions 03E35: Consistency and independence results 03E40: Other aspects of forcing and Boolean-valued models

Keywords
axiom of choice ZFA permutation models

Citation

Hall, Eric J. Permutation Models and SVC. Notre Dame J. Formal Logic 48 (2007), no. 2, 229--235. doi:10.1305/ndjfl/1179323265. https://projecteuclid.org/euclid.ndjfl/1179323265


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References

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