Timeline for Montague's Reflection Principle and Compactness Theorem
Current License: CC BY-SA 2.5
11 events
| when toggle format | what | by | license | comment | |
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| Apr 13, 2017 at 12:57 | history | edited | CommunityBot |
replaced http://mathoverflow.net/ with https://mathoverflow.net/
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| Apr 20, 2010 at 15:03 | comment | added | Joel David Hamkins | François, no problem! I also find it to be a very cool fact. | |
| Mar 20, 2010 at 19:29 | comment | added | François G. Dorais | @Joel: By the way, I'm sorry for "stealing" your cool fact. I waited a while before posting it, but you didn't seem to be around at the time and I couldn't bear not mentioning it... | |
| Mar 20, 2010 at 19:25 | comment | added | François G. Dorais | @oktan: It's a wonderful question that puzzles every novice set theorist at some point. I'm glad you gave us the opportunity to answer it here. | |
| Mar 20, 2010 at 19:19 | history | edited | François G. Dorais | CC BY-SA 2.5 |
improved wording
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| Mar 20, 2010 at 16:30 | comment | added | Stefan Hoffelner | Thank you again. Your answers were really an eye-opener. Made my day | |
| Mar 20, 2010 at 11:58 | comment | added | Joel David Hamkins | Oktan, what François argued was that for any (standard) n, the people in M agree that the size n fragment of ZFC is consistent. But since M has no nonstandard natural numbers, this exhausts all of the natural numbers of M, and so M will believe the universal statement, that all finite fragments of ZFC are consistent. And this implies that ZFC is consistent. You wouldn't be able to make these last steps of the argument if M had a nonstandard omega, precisely because as Sridhar and François point out, you only get the Reflection Principle for standard finitely many statements. | |
| Mar 20, 2010 at 10:16 | comment | added | Stefan Hoffelner | Thank you very much for your answer. There is something I don't understand though: In your third break you write:" ...by Montague people living in $M$ believe that $\{ \phi_{0},...,\phi_{n} \}$ has a model for each $n< \omega$." And now you conclude with compactness that $M$ thinks there is a model of ZFC. But as Sridhar pointed out, ZFC does not prove " for any finite subset of axioms ZFC, there exists a model". Hence $M$ does not believe that $\{ \phi_{0},..,\phi_{n} \}$ has a model for each $n< \omega$ and one cannot derive that $M$ thinks that "there is a model of ZFC". Am I wrong? | |
| Mar 20, 2010 at 8:54 | vote | accept | Stefan Hoffelner | ||
| Mar 20, 2010 at 10:17 | |||||
| Mar 19, 2010 at 23:14 | history | edited | François G. Dorais | CC BY-SA 2.5 |
added link & changed some wording
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| Mar 19, 2010 at 22:50 | history | answered | François G. Dorais | CC BY-SA 2.5 |