Timeline for Ideals of statements?
Current License: CC BY-SA 2.5
11 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Apr 28, 2010 at 15:10 | vote | accept | David Spivak | ||
| Apr 28, 2010 at 14:30 | comment | added | Joel David Hamkins | Ah, now I see... | |
| Apr 28, 2010 at 14:14 | comment | added | François G. Dorais | You're right, I shouldn't have pulled a BCnrd. The second sentence of my answer should explain. | |
| Apr 28, 2010 at 14:09 | answer | added | François G. Dorais | timeline score: 9 | |
| Apr 28, 2010 at 12:46 | comment | added | Joel David Hamkins | François, please add your answer as an answer. | |
| Apr 28, 2010 at 8:18 | comment | added | François G. Dorais | Yes, of course, the algebraic aspects of logic have been very well studied. There is one important thing though, you might want to ask for your ideals to be closed under logical equivalence too. Otherwise, statements of length 17 or more form a rather silly ideal. With this change, your ideals are called deductively closed theories. The space you're describing is basically the Stone space of the Lindenbaum algebra, or the space of types, which is widely studied in model theory. The Compactness Theorem takes a very nice form when stated in this language. | |
| Apr 28, 2010 at 7:53 | history | edited | David Spivak | CC BY-SA 2.5 |
added 200 characters in body
|
| Apr 28, 2010 at 7:47 | history | edited | David Spivak | CC BY-SA 2.5 |
added 106 characters in body
|
| Apr 28, 2010 at 7:20 | comment | added | Qiaochu Yuan | Some Wikipedia pages that might be relevant: en.wikipedia.org/wiki/Ideal_%28order_theory%29, en.wikipedia.org/wiki/Galois_connection . | |
| Apr 28, 2010 at 7:10 | history | edited | David Spivak | CC BY-SA 2.5 |
added 3 characters in body; added 8 characters in body; added 46 characters in body; added 67 characters in body
|
| Apr 28, 2010 at 7:01 | history | asked | David Spivak | CC BY-SA 2.5 |