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.
Citation
Eric J. Hall. "Permutation Models and SVC." Notre Dame J. Formal Logic 48 (2) 229 - 235, 2007. https://doi.org/10.1305/ndjfl/1179323265
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