Timeline for Existence of prime ideals and Axiom of Choice.
Current License: CC BY-SA 4.0
8 events
| when toggle format | what | by | license | comment | |
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| Mar 2 at 16:41 | history | edited | Martin Sleziak | CC BY-SA 4.0 |
minor typos
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| Apr 13, 2017 at 12:58 | history | edited | CommunityBot |
replaced http://mathoverflow.net/ with https://mathoverflow.net/
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| Jan 25, 2016 at 10:56 | comment | added | ACL | @LaurentMoret-Bailly: The PhD Thesis of Hervé Perdry, hlombardi.free.fr/liens/TheseHervePerdry.pdf, took care of the question of constructive noetherianity by rewriting the definition of noetherian as “every increasing sequence pauses” (meaning “is not strictly increasing”). | |
| Jun 2, 2012 at 14:08 | comment | added | Martin Brandenburg | You're right ... perhaps it doesn't work at all that way. | |
| Jun 2, 2012 at 11:53 | comment | added | Laurent Moret-Bailly | One should be careful that the Dependent Choice Axiom is needed to prove that ``every increasing sequence terminates'' implies the existence of maximal elements. So, can the proof of Hilbert's theorem be arranged to take care of this? | |
| Jun 1, 2012 at 15:17 | comment | added | Martin Brandenburg | Yes, but that's not really clever. The equivalence simplifies the problem right ahead. We shouldn't care about "Cohen's Theorem" (as the OP called it) at all. | |
| Jun 1, 2012 at 14:59 | comment | added | François G. Dorais | You can get the result as stated without localization and quotient by adding the axioms $p_a$ for $a \in I$ and $\lnot p_b$ for $b \in S$. It looks like this does not affect the argument for finite consistency. | |
| Jun 1, 2012 at 14:16 | history | answered | Martin Brandenburg | CC BY-SA 3.0 |