Timeline for Possible no standard use of replacement axiom
Current License: CC BY-SA 3.0
9 events
| when toggle format | what | by | license | comment | |
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| Sep 24, 2016 at 20:51 | vote | accept | Carlos Freites | ||
| May 26, 2014 at 5:18 | comment | added | Carlos Freites | However I go further, my "NUCLEUS" develop the minimum to arrive to the Complete Field definition, then I take the Real numbers (and 0,+,1,*, etc) as a constant that is a Complete Field. This may be not standard, but works very well. | |
| May 25, 2014 at 19:23 | history | edited | Carlos Freites | CC BY-SA 3.0 |
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| May 25, 2014 at 14:48 | comment | added | Joel David Hamkins | Yes, and so the point is that you can introduce any such kind of terms, over any theory that proves that there are such sets realizing the terms definitions, and the new theory will be conservative over the original theory. In a sense, mathematicians and set theorist already do this instinctively, since one almost never sees assertions written out in the fundamental language of set theory (and nobody wants to see such assertions). Rather, we all pepper our mathematical reasoning with defined terms and expressions. And this is perfectly safe, for the reasons in the answer to which I linked. | |
| May 25, 2014 at 14:43 | comment | added | Carlos Freites | Exactly, Joel. The third paragraph of the answer 4, state "One might try to make all of the axioms of ZFC into term-forming operators, so that instead of saying "there exists a set with no elements" there would be a specified term ∅ and an axiom saying "∅ has no elements," and likewise for pairings, unions, replacement, etc... " and it is exactly what I have done in my ZFC formulation, do I have terms in it. | |
| May 25, 2014 at 7:11 | comment | added | Joel David Hamkins | See related question about introduction of terms in set theory: mathoverflow.net/a/12405/1946 | |
| May 24, 2014 at 20:34 | review | First posts | |||
| May 24, 2014 at 20:50 | |||||
| May 24, 2014 at 20:21 | answer | added | Andreas Blass | timeline score: 2 | |
| May 24, 2014 at 20:12 | history | asked | Carlos Freites | CC BY-SA 3.0 |