Timeline for Can there exists a model of ZFC with permutation that sends successor infinite stages to their predecessors?

12 events

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Sep 22 at 11:51	comment	added	Zuhair Al-Johar		@I see, I meant we can have $M$ if we state it in terms of $\sf Z$ instead of $\sf ZF$. Even if we have $V_\omega^M$ I think we can arrange for $j[V_\omega^M]$ to be some subset of $V_\omega^M$ such that the complement of $j[V_\omega^M]$ is infinite and thus has a room for images of extra-elements of $V_{\omega+1}$ under $j$.
Sep 21 at 21:37	comment	added	Joel David Hamkins		Oh, I thought you meant the argument I gave can be used also with models of Z.
Sep 21 at 20:37	comment	added	Zuhair Al-Johar		Well the magic word in the question is "can", $V_{\omega+\omega}$ is a model of $\sf Z$, the point is that we don't want $V_{\omega+\omega+1}$ to be there, because of the exhaustive argument you depicted.
Sep 21 at 20:22	comment	added	Joel David Hamkins		No, because even $V_\omega$ doesn't necessarily exist in Z, let alone $V_{\omega+\omega+1}$.
Sep 21 at 17:43	comment	added	Zuhair Al-Johar		so this can be used if $M$ is a model of $\sf Z$.
Sep 21 at 17:40	vote	accept	Zuhair Al-Johar
Sep 21 at 15:09	history	undeleted	Joel David Hamkins
Sep 21 at 15:09	history	edited	Joel David Hamkins	CC BY-SA 4.0	added 137 characters in body
Sep 21 at 15:03	history	edited	Joel David Hamkins	CC BY-SA 4.0	added 137 characters in body
Sep 21 at 15:02	history	deleted	Joel David Hamkins		via Vote
Sep 21 at 14:38	history	edited	Joel David Hamkins	CC BY-SA 4.0	added 405 characters in body
Sep 21 at 14:19	history	answered	Joel David Hamkins	CC BY-SA 4.0