Timeline for Intersection of compact sets in the unit interval
Current License: CC BY-SA 3.0
8 events
| when toggle format | what | by | license | comment | |
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| Oct 1, 2013 at 11:50 | comment | added | Ramiro de la Vega | @TaQ: I wouldn´t call $MA_{\aleph_1}$ "exotic"; after all it is just a "mild" generalization of Baire´s category theorem. It is also the first axiom one usually looks at as an alternative to $CH$, since $\lnot CH$ alone is just too weak. | |
| Oct 1, 2013 at 11:35 | comment | added | TaQ | @ Ramiro de la Vega: Thanks for the clarification. Both answers are interesting and useful although I originally was hoping that the positive answer would be a consequence of some less "exotic" axiom. | |
| Sep 30, 2013 at 23:24 | comment | added | Ramiro de la Vega | @TaQ: I edited my answer to clarify these points. | |
| Sep 30, 2013 at 23:22 | history | edited | Ramiro de la Vega | CC BY-SA 3.0 |
added 336 characters in body
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| Sep 30, 2013 at 22:37 | comment | added | TaQ | @ Ramiro de la Vega. Reading the wikipedia definition en.wikipedia.org/wiki/… , I am trying to understand how your reasoning fits in it. What is a "centered" subset, and what is wp's $D$ in your setting? Why is $Q$ uncountable? | |
| Sep 29, 2013 at 16:00 | comment | added | Noel Vaillant | @LevBorisov it is a theorem of ZFC that $\mathtt{MA}({\bf c})$ fails. So if CH holds, then $\mathtt{MA}(\aleph_{1})$ will fail. If $\lnot$CH holds, then $\mathtt{MA}(\aleph_{1})$ is consistent with ZFC+$\lnot$CH. Just reading on wiki about Martin's axioms. | |
| Sep 29, 2013 at 14:43 | comment | added | Lev Borisov | So how to reconcile the two answers? | |
| Sep 29, 2013 at 2:57 | history | answered | Ramiro de la Vega | CC BY-SA 3.0 |