Timeline for Can "$\exists\mathcal{X}(R\cong C(\mathcal{X}))$" be expressed in "large" infinitary second-order logic?
Current License: CC BY-SA 4.0
9 events
| when toggle format | what | by | license | comment | |
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| S Jun 9, 2022 at 19:03 | history | bounty ended | CommunityBot | ||
| S Jun 9, 2022 at 19:03 | history | notice removed | CommunityBot | ||
| Jun 2, 2022 at 2:26 | comment | added | Simon Henry | Oh. The point I am missing is that you want a characterization of rings of functions, and not of bounded functions. Sorry. got it. | |
| Jun 2, 2022 at 2:20 | comment | added | Simon Henry | I don't quite see why the Gelfand duality style characterization cannot be formulated in second order logic. Could you clarify what part of the characterization doesn't work ? working with complex number for simplicity, I don't see why "there exists a norm making R a C* algebra" isn't working : Completeness for a fixed norm is definable in infinitary second order logic, the rest of the C* algebra axiom are just equation and "there exist a norm" can be phrased in terms of existence of a "unit ball" with certain property... What point am I messing ? | |
| Jun 1, 2022 at 18:21 | history | edited | user44143 | CC BY-SA 4.0 |
added reference for $FOL_{\infty,\infty}$ in Stanford Encyclopedia of Philosophy, removed some parentheses, shortened an overly long sentence
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| S Jun 1, 2022 at 18:00 | history | bounty started | Noah Schweber | ||
| S Jun 1, 2022 at 18:00 | history | notice added | Noah Schweber | Draw attention | |
| May 28, 2022 at 20:58 | history | edited | Noah Schweber | CC BY-SA 4.0 |
added 31 characters in body
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| May 28, 2022 at 20:49 | history | asked | Noah Schweber | CC BY-SA 4.0 |