Timeline for Can we prove set theory is consistent?
Current License: CC BY-SA 2.5
4 events
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| Apr 28, 2010 at 19:37 | comment | added | kakaz | Infinitely but computable. By Gentzen construction You may produce theory which can prove its consistence, but at cost of large number of axioms acquisition. I do nor write about finite number of rules...only about proof of consistence which uses finite (or computable) number of it. Do You accept infinite proofs? Formalized system means that there is certain number of axioms and rules of inference. It is important requirements, because if You during proving something change the rules of the game, You cannot use Goedel Theorem at all... | |
| Apr 28, 2010 at 11:20 | comment | added | Andrea Ferretti | I don't think the problem is the finitess of the rules. Theories are certainly allowed to have infinitely many axioms (e.g. the theory of fields of characteristic 0). | |
| Apr 28, 2010 at 11:06 | history | edited | kakaz | CC BY-SA 2.5 |
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| Apr 27, 2010 at 19:33 | history | answered | kakaz | CC BY-SA 2.5 |