Permutation Models and SVC
Hall, Eric J.
Notre Dame J. Formal Logic, Tome 48 (2007) no. 1, p. 229-235 / Harvested from Project Euclid
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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.
Publié le : 2007-04-14
Classification:  axiom of choice,  ZFA,  permutation models,  03E25,  03E35,  03E40 
@article{1179323265,
     author = {Hall, Eric J.},
     title = {Permutation Models and SVC},
     journal = {Notre Dame J. Formal Logic},
     volume = {48},
     number = {1},
     year = {2007},
     pages = { 229-235},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1179323265}
}

Hall, Eric J. Permutation Models and SVC. Notre Dame J. Formal Logic, Tome 48 (2007) no. 1, pp.  229-235. http://gdmltest.u-ga.fr/item/1179323265/