Timeline for Is there a model of ZF+ACC where transfer fails for the definable hyperreals?
Current License: CC BY-SA 3.0
10 events
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| Jul 5, 2017 at 7:48 | comment | added | Mikhail Katz | @JoelDavidHamkins, yes, precisely, as far as I understand it. | |
| Jul 5, 2017 at 7:48 | comment | added | Mikhail Katz | @NoahSchweber, I think both are definable. The point is that this is not an ultrafilter on $\mathbb N$; obviously there aren't any definable ones. But I will check with my coauthors to see if this is correct. | |
| Jul 4, 2017 at 17:33 | comment | added | Joel David Hamkins | Is the idea that you are taking a direct limit of all ultrapowers and thereby avoiding the need to pick a particular one? | |
| Jul 4, 2017 at 16:09 | comment | added | Noah Schweber | "we get the required definable ultrafilter" Do you really mean a definable ultrafilter, or definable *hyperreal extension"? | |
| Jul 4, 2017 at 14:02 | comment | added | Mikhail Katz | By the way no mention of "if/else" clauses appears in the article; it was my way (as you point out, imperfect) of characterizing the construction. | |
| Jul 4, 2017 at 13:43 | comment | added | Mikhail Katz | @JoelDavidHamkins, I would have liked to say that our formula works in intuitionistic logic but I don't know enough about it to be able to make such a claim. Perhaps some of the experts here can help. It any rate it is a completely deterministic explicit construction of an ultrafilter by specifying a suitable ordinal and considering all surjections from this ordinal to free ultrafilters on N. This gives an index set. By tensoring together different ultrapowers and using "threads" (Keisler's terminology) in a direct limit of all these tensors, we get the required definable ultrafilter. | |
| Jul 4, 2017 at 12:25 | comment | added | Joel David Hamkins | Do you mean something precise and robust when you say "without if/else clauses"? For example, is your definition a positive formula? Otherwise, one could imagine simply disguising an if/else clause with a logical variant, but of course that is not what you mean. So what is it that you mean? | |
| Jul 4, 2017 at 11:57 | history | edited | Mikhail Katz | CC BY-SA 3.0 |
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| Jul 4, 2017 at 8:10 | history | edited | Mikhail Katz | CC BY-SA 3.0 |
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| Jul 4, 2017 at 8:03 | history | answered | Mikhail Katz | CC BY-SA 3.0 |