Notre Dame Journal of Formal Logic

Permutation Models and SVC

Eric J. Hall


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

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

First available in Project Euclid: 16 May 2007

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

axiom of choice ZFA permutation models


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

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