Timeline for Set theory and Model Theory
Current License: CC BY-SA 2.5
6 events
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| Jan 16, 2023 at 20:36 | comment | added | Chill2Macht | @Kevin you are not entirely wrong to be concerned, because e.g. we can not use the metatheory ZFC to define a "truth predicate" for the object theory ZFC, by Tarski's theorem on the nondefinability of truth / Godel's incompleteness theorem (what the answer I believe is referring to by "Godel's celebrated result" -- Godel has several). E.g. you can't define in ZFC a "set of all coded formulas, where the formula being coded is true in ZFC". Is that what you're asking? But that doesn't stop us encoding the axioms of ZFC as a set inside ZFC, which I think is all that the answer is claiming. | |
| Aug 27, 2021 at 1:04 | comment | added | Kevin | You suggest model theory uses ZFC to describe a set of "coded formulas". Is this set itself able to be expressed in a coded formula? If so, it has itself as an element, if not, then how are we justified in using ZFC to construct such a set? | |
| Apr 30, 2010 at 14:13 | history | edited | Stefan Hoffelner | CC BY-SA 2.5 |
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| Apr 30, 2010 at 13:59 | history | edited | Stefan Hoffelner | CC BY-SA 2.5 |
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| Apr 30, 2010 at 11:49 | history | edited | Stefan Hoffelner | CC BY-SA 2.5 |
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| Apr 30, 2010 at 11:26 | history | answered | Stefan Hoffelner | CC BY-SA 2.5 |