Timeline for Characterization of $\kappa$-closed forcings
Current License: CC BY-SA 3.0
4 events
| when toggle format | what | by | license | comment | |
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| Sep 19, 2012 at 7:24 | comment | added | François G. Dorais | The papers by Foreman and Vojtáš have what you want but the results are partial. Their results are also optimal, in some sense, because of Zapletal's example. Zapletal's example shows that it is generally hard to tell which complete Boolean algebras have a $\kappa$-closed dense subset. | |
| Sep 19, 2012 at 6:07 | comment | added | Monroe Eskew | However, a dense embedding from one seperative partial order to another implies that their respective boolean completions are isomorphic. (right?) For this question I am more interested in combinatorial properties of the boolean completion (because it's the canonical representiative of the forcing-equivalence class) vs. things satisfied by the generic extension. I'm not sure if I can give a rigorous definition of what I'm looking for, but the equivalent formulations of distributivity properties, plus things like weak $(\lambda,\kappa)$-saturation seem to capture the spirit. | |
| Sep 19, 2012 at 5:40 | history | edited | François G. Dorais | CC BY-SA 3.0 |
minor edits
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| Sep 19, 2012 at 5:26 | history | answered | François G. Dorais | CC BY-SA 3.0 |