Forcing under Anti-Foundation Axiom: An expression of the stalks
dc.contributor.author | Kentaro, Sato | en_US |
dc.date.accessioned | 2007-07-11T18:17:07Z | |
dc.date.available | 2007-07-11T18:17:07Z | |
dc.date.issued | 2006-06 | en_US |
dc.identifier.citation | Kentaro, Sato (2006). "Forcing under Anti-Foundation Axiom: An expression of the stalks." Mathematical Logic Quarterly 52(3): 295-314. <http://hdl.handle.net/2027.42/55242> | en_US |
dc.identifier.issn | 0942-5616 | en_US |
dc.identifier.issn | 1521-3870 | en_US |
dc.identifier.uri | https://hdl.handle.net/2027.42/55242 | |
dc.description.abstract | We introduce a new simple way of defining the forcing method that works well in the usual setting under FA, the Foundation Axiom, and moreover works even under Aczel's AFA, the Anti-Foundation Axiom. This new way allows us to have an intuition about what happens in defining the forcing relation. The main tool is H. Friedman's method of defining the extensional membership relation ∈ by means of the intensional membership relation. Analogously to the usual forcing and the usual generic extension for FA-models, we can justify the existence of generic filters and can obtain the Forcing Theorem and the Minimal Model Theorem with some modifications. These results are on the line of works to investigate whether model theory for AFA-set theory can be developed in a similar way to that for FA-set theory. Aczel pointed out that the quotient of transition systems by the largest bisimulation and transition relations have the essentially same theory as the set theory with AFA. Therefore, we could hope that, by using our new method, some open problems about transition systems turn out to be consistent or independent. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) | en_US |
dc.format.extent | 258785 bytes | |
dc.format.extent | 3118 bytes | |
dc.format.mimetype | application/pdf | |
dc.format.mimetype | text/plain | |
dc.publisher | WILEY-VCH Verlag | en_US |
dc.subject.other | Mathematics and Statistics | en_US |
dc.title | Forcing under Anti-Foundation Axiom: An expression of the stalks | 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 | Research Center for Verification and Semantics (CVS), National Institute of Advanced Industrial Science and Technology (AIST), Japan ; Department of Mathematics, University of Michigan, Ann Arbor, Michigan, 48109-1043, USA ; Graduate School of Science and Technology, Kobe University, Rokkodai-cho, Nada-ku, Kobe, 657-8501, Japan | en_US |
dc.description.bitstreamurl | http://deepblue.lib.umich.edu/bitstream/2027.42/55242/1/295_ftp.pdf | en_US |
dc.identifier.doi | http://dx.doi.org/10.1002/malq.200410060 | en_US |
dc.identifier.source | Mathematical Logic Quarterly | en_US |
dc.owningcollname | Interdisciplinary and Peer-Reviewed |
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