Timeline for Hausdorff and Naive Set Theory
Current License: CC BY-SA 4.0
8 events
| when toggle format | what | by | license | comment | |
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| Nov 27, 2023 at 17:58 | vote | accept | Thomas Benjamin | ||
| Oct 6, 2023 at 16:00 | history | edited | Glorfindel | CC BY-SA 4.0 |
broken link fixed, cf. https://meta.mathoverflow.net/q/5301/70594
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| Jan 27, 2013 at 15:53 | comment | added | Thomas Benjamin | The actual title of the Friedman paper is "The Axiomatization of Set Theory by Extensionality, Separation, and Reducibility". Sorry. | |
| Jan 27, 2013 at 14:27 | comment | added | Thomas Benjamin | @Andres: Since ZF via Separation and Replacement is infinitely axiomatizable, any finite (or infinite) list of axioms derived from the Separation and Replacement schema are fragments and might be deemed falling short of the mark (I hope that this is not too silly or stupid a remark--if it is, my apologies...). Could, for example, one show that large cardinal axioms could not be construed as instances of replacement or separation (I'm thinking of Harvey Friedman's paper, "The Axiomatization of Set Theory by Extensionality, Separation, and Replacement")? Is this just a silly idea? | |
| Jan 27, 2013 at 13:52 | comment | added | Thomas Benjamin | @John: 'Lirbert' should be "Thierry Libert". Sorry. | |
| Jan 27, 2013 at 13:48 | comment | added | Thomas Benjamin | @John: Nice answer. I looked through Blumberg's review and thoroughly enjoyed it! Another good article along the same line is Peter Koepke's "Felix Hausdorff and the Foundations of Mathematics". In it, regarding the paradoxes, Koepke quotes Hausdorff as saying (quoted from the Grundzuge), "we want to admit the naive notion of set, but observing the restrictions which cut off the way to that [the--my comment] paradox[es]." The works of Skolem, Esser, C.C. Chang, Hinnion, Brady, P.C. Gilmore, Lirbert, and others still researching Naive Set Theory come to mind.... | |
| Jan 26, 2013 at 2:48 | comment | added | Andrés E. Caicedo | The original axiomatization of set theory missed foundation and replacement, which are key components of our current intuitive picture of the set theoretic universe. The Zermelo-Fraenkel list misses large cardinals. And so on. Perhaps the idea that the axiomatization was premature was not that off the mark. | |
| Jan 26, 2013 at 2:37 | history | answered | John Stillwell | CC BY-SA 3.0 |