Timeline for Elementary submodels of V
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Aug 3, 2012 at 13:41 | vote | accept | curious | ||
| Aug 3, 2012 at 13:41 | |||||
| Aug 2, 2012 at 15:22 | history | edited | Noah Schweber | CC BY-SA 3.0 |
Improved statement
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| Aug 2, 2012 at 15:22 | comment | added | Noah Schweber | Oh, good point! Fixed. | |
| Aug 2, 2012 at 15:16 | comment | added | François G. Dorais | By the way, the parenthetical remark doesn't really need choice. If $(S_0,{\in}) \vDash T$ then $\lbrace S \in S_0 : (S,{\in}) \vDash T \rbrace$ (which exists by comprehension) has no ${\in}$-minimal element, which contradicts foundation. | |
| Aug 2, 2012 at 7:14 | comment | added | curious | Excellent points. In reference to the first point, I suppose I should phrase the question semantically - is there some sort of axiom $A$ such that in every model of $A$, $C$ is true. Assuming that we are interested in (large cardinal) axioms that are first order definable and hold true in at least one well-founded model, your argument shows that the answer is no. | |
| Aug 2, 2012 at 6:36 | history | answered | Noah Schweber | CC BY-SA 3.0 |