Forcing under Anti-Foundation Axiom: An expression of the stalks

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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 http://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.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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