Timeline for Is any axiom system for sets categorical?
Current License: CC BY-SA 3.0
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Aug 20, 2014 at 14:47 | comment | added | Lehs | @bof: It feels good to know that I can trust on the countables. | |
| Aug 20, 2014 at 14:44 | comment | added | Lehs | @Asaf Karagila: You are right. The "sets" in our minds are just mental models that stimulates the fantasy, but must be supervised and cleared by the formal rules. | |
| Aug 20, 2014 at 11:03 | comment | added | Asaf Karagila♦ | @Lehs: Almost, but not quite. We have axioms just so we can always ensure that certain properties are true, and then we work with these properties. This is exactly to ensure that other people who might interpret these notions differently still agree with you about core principles in a way which is relatively absolute between one person to another (meaning I can convince you why my proof work if we sit carefully enough and overview the details). | |
| Aug 20, 2014 at 10:59 | comment | added | Asaf Karagila♦ | @bof: As is any countable model of a countable theory (I don't recall the reference for the theorem, but Scott analysis might be good keywords to start looking). | |
| Aug 20, 2014 at 10:07 | comment | added | bof | But a countable model of set theory can be characterized up to isomorphism by a single first-order sentence of infinite length, right? | |
| Aug 20, 2014 at 10:00 | vote | accept | Lehs | ||
| Aug 20, 2014 at 9:57 | comment | added | Lehs | So the first order definitions of set theory only provide a class of relations from which each mathematician make a choice $\in$ and hope that all other mathematician make the same choice (or doesn't think about it)? And it doesn't matter? | |
| Aug 20, 2014 at 9:34 | history | answered | Asaf Karagila♦ | CC BY-SA 3.0 |