Complete topoi representing models of set theory
dc.contributor.author | Blass, Andreas | en_US |
dc.contributor.author | Scedrov, Andrej | en_US |
dc.date.accessioned | 2006-04-10T15:13:28Z | |
dc.date.available | 2006-04-10T15:13:28Z | |
dc.date.issued | 1992-05-06 | en_US |
dc.identifier.citation | Blass, Andreas, Scedrov, Andre (1992/05/06)."Complete topoi representing models of set theory." Annals of Pure and Applied Logic 57(1): 1-26. <http://hdl.handle.net/2027.42/30052> | en_US |
dc.identifier.uri | http://www.sciencedirect.com/science/article/B6TYB-45F5R5T-5/2/eed8175516fe472b81d293519cb237ff | en_US |
dc.identifier.uri | https://hdl.handle.net/2027.42/30052 | |
dc.description.abstract | By a model of set theory we mean a Boolean-valued model of Zermelo-Fraenkel set theory allowing atoms (ZFA), which contains a copy of the ordinary universe of (two-valued,pure) sets as a transitive subclass; examples include Scott-Solovay Boolean-valued models and their symmetric submodels, as well as Fraenkel-Mostowski permutation models. Any such model M can be regarded as a topos. A logical subtopos of M is said to represent M if it is complete and its cumulative hierarchy, as defined by Fourman and Hayashi, coincides with the usual cumulative hierarchy of M. We show that, although M need not be a complete topos, it has a smallest complete representing subtopos, and we describe this subtopos in terms of definability in M. We characterize, again in terms of definability, those models M whose smallest representing topos is a Grothendieck topos. Finally, we discuss the extent to which a model can be reconstructed when its smallest representing topos is given. | en_US |
dc.format.extent | 1952807 bytes | |
dc.format.extent | 3118 bytes | |
dc.format.mimetype | application/pdf | |
dc.format.mimetype | text/plain | |
dc.language.iso | en_US | |
dc.publisher | Elsevier | en_US |
dc.title | Complete topoi representing models of set theory | en_US |
dc.type | Article | en_US |
dc.rights.robots | IndexNoFollow | en_US |
dc.subject.hlbsecondlevel | Mathematics | en_US |
dc.subject.hlbtoplevel | Science | en_US |
dc.description.peerreviewed | Peer Reviewed | en_US |
dc.contributor.affiliationum | Mathematics Department, University of Michigan, Ann Arbor, MI 48109, USA | en_US |
dc.contributor.affiliationother | Mathematics Department, University of Pennsylvania, Philadelphia, PA 19104, USA | en_US |
dc.description.bitstreamurl | http://deepblue.lib.umich.edu/bitstream/2027.42/30052/1/0000420.pdf | en_US |
dc.identifier.doi | http://dx.doi.org/10.1016/0168-0072(92)90059-9 | en_US |
dc.identifier.source | Annals of Pure and Applied Logic | en_US |
dc.owningcollname | Interdisciplinary and Peer-Reviewed |
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