Timeline for A question regarding forcing in $NGBC^{-f}$+$BAFA$
Current License: CC BY-SA 3.0
13 events
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| Oct 10, 2015 at 22:23 | comment | added | Noah Schweber | By the way, fun fact, another non-foundational theory which can make sense of forcing is Quine's New Foundations! math.boisestate.edu/~holmes/holmes/informal_forcing | |
| Oct 10, 2015 at 22:22 | comment | added | Noah Schweber | I don't - this isn't material I'm at all familiar with. I sat down with a student a year ago to try to work out forcing over $ZF^{-f}$ and ran into difficulties, so when I saw this question my interest was piqued, but I don't actually know anything here. | |
| Oct 10, 2015 at 21:54 | comment | added | Thomas Benjamin | @NoahSchweber: Thanks for the links in your comments. I am especially interested in arxiv.org/pdf/0712.1968.pdf since it directly (favorably) mentions Boffa. The problem is, is that Johnson ends his paper in the middle (so to speak). Do you know if he has the completion of his forcing method in another paper? If so, please provide the link to that paper also. | |
| Oct 10, 2015 at 16:19 | history | edited | Stefan Kohl♦ |
Added top-level tag.
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| Oct 10, 2015 at 15:28 | review | Close votes | |||
| Oct 15, 2015 at 17:18 | |||||
| Oct 10, 2015 at 6:49 | comment | added | Thomas Benjamin | (cont.) definition with 'class'. If this idea is wrong-headed, please let me know. Thanks. | |
| Oct 10, 2015 at 6:47 | comment | added | Thomas Benjamin | @NoahSchweber: I care about the class-theoretic version for the same reason that Hamkins and others say that $NGBC$ can better capture the import of the Kunen inconsistency than can $ZFC$+'$j$'. If $NGBC$ can better capture the import of the Kunen inconsistency, then perhaps class forcing would be the better method for constructing models of $NGB^{-f}$+ $BAFA$+$\lnot$$AC$. Since I am not at all sure about this, I added class forcing (in parentheses) for completeness. In which case, one might want to adjust the definition of $BAFA$ to suit--replace every occurrence of 'set' in that | |
| Oct 10, 2015 at 6:17 | history | edited | Thomas Benjamin | CC BY-SA 3.0 |
added more information for clarification
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| Oct 10, 2015 at 5:22 | comment | added | Noah Schweber | Actually, this article might be more directly related: arxiv.org/pdf/0712.1968.pdf. See also users.auth.gr/tzouvara/Texfiles.htm/forcing.pdf. (By the way, is there a reason you care about the class-theoretic version instead of the set-theoretic version?) | |
| Oct 10, 2015 at 5:19 | comment | added | Noah Schweber | I think the first thing to do is to properly define "forcing" over models of BAFA! Note that even forcing over models of AFA - a much tamer antifoundation axiom - took real effort: see S. Kentaro's article onlinelibrary.wiley.com/doi/10.1002/malq.200410060/abstract. The problem is that without Foundation it's not clear how to define a name or the interpretation of a name. | |
| Oct 9, 2015 at 17:15 | comment | added | Monroe Eskew | Suggested improvement: Give definitions of the theories. | |
| Oct 9, 2015 at 7:20 | history | edited | Thomas Benjamin | CC BY-SA 3.0 |
added word for clarification
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| Oct 9, 2015 at 6:49 | history | asked | Thomas Benjamin | CC BY-SA 3.0 |