Permutation Models and SVC

Notre Dame Journal of Formal Logic 48 (2):229-235 (2007)
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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

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Citations of this work

Boolean-Valued Models of Set Theory with Urelements.Xinhe Wu & Bokai Yao - 2024 - Notre Dame Journal of Formal Logic 65 (2):203-227.

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References found in this work

The Axiom of Choice.Thomas J. Jech - 1973 - Amsterdam, Netherlands: North-Holland.
A Characterization of Permutation Models in Terms of Forcing.Eric J. Hall - 2002 - Notre Dame Journal of Formal Logic 43 (3):157-168.

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