Timeline for Automorphisms of the hyperreals over the rationals and nontrivial automorphism groups

7 events

when toggle format	what		by	license	comment
Dec 31, 2016 at 22:51	history	edited	Joel David Hamkins	CC BY-SA 3.0	added 49 characters in body
Dec 31, 2016 at 21:03	comment	added	Joel David Hamkins		Correction: I should have said finitely-generated subfield; of course, it is countably infinite.
Dec 31, 2016 at 19:14	comment	added	Todd Trimble		Oh sure; thanks. I rather prefer that formulation.
Dec 31, 2016 at 19:12	comment	added	Joel David Hamkins		One could argue like this: that theory (the elementary diagram of $F$ plus the assertion that $\pi$ is a nontrivial automorphism) is consistent, because every finite part of the theory is consistent, since any finite subtheory makes reference to only finitely many particular elements of $F$, which generate a finite subfield, and then reduce to the computable saturation argument in the countable case. So, no forcing. I think almost any model theory book will prove the existence of sufficiently homogeneous models, and that is what I'm doing.
Dec 31, 2016 at 18:49	comment	added	Todd Trimble		Is it possible to rewrite your penultimate paragraph so as to make no reference to forcing extensions, but instead appeal to pure model theory?
Dec 31, 2016 at 13:22	history	edited	Joel David Hamkins	CC BY-SA 3.0	added 135 characters in body
Dec 31, 2016 at 13:09	history	answered	Joel David Hamkins	CC BY-SA 3.0