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Feb 16, 2020 at 2:00 history edited Dmytro Taranovsky CC BY-SA 4.0
update reflecting current knowledge
Jan 20, 2020 at 15:44 comment added Dmytro Taranovsky @AliEnayat Unlike the Wholeness Axiom (which it superficially resembles), the theory only appears to require separation below sets moved by $j$ since without the critical point it appears that none of the sets moved by $j$ need to be definable.
Jan 20, 2020 at 5:28 comment added Ali Enayat Your self-embedding axiom seems close to Corazza's Wholeness axiom, see en.wikipedia.org/wiki/Wholeness_axiom
Jan 19, 2020 at 16:43 history asked Dmytro Taranovsky CC BY-SA 4.0