Timeline for When does the generalized Cantor space embed in a $\kappa$-compact space
Current License: CC BY-SA 3.0
9 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| May 20, 2016 at 17:49 | comment | added | Philipp Lücke | 1. The existence of weak Kurepa trees at all uncountable regular in L already follows from Solovay's argument mentioned in item 3. The cited paper sketches a class forcing construction that adds a weak Kurepa tree at every inaccessible cardinal, while preserving many large cardinals. 2. Yes. This short argument is, for example, contained in Section 7 of the paper cited in item 2. | |
| May 16, 2016 at 13:17 | comment | added | Boaz Tsaban | @Philipp: I would appreciate some additional clarifications: 1. Remark (1) on page 33 of the paper you cited in your item 4: In $L$, is there a weak Kurepa tree for all uncountable regular (inaccessible?) $\kappa$? 2. Does your item 3 assert that the existence of a weak Kurepa tree for $\kappa$ imply $2^\kappa$ does not embed in every $\kappa$-compact space? | |
| Apr 19, 2016 at 11:53 | history | bounty ended | Boaz Tsaban | ||
| Apr 19, 2016 at 11:53 | vote | accept | Boaz Tsaban | ||
| Apr 17, 2016 at 15:31 | comment | added | Yair Hayut | If $T$ is a tree that contains a subtree isomorphic to $2^{<\kappa}$ then $\text{Add}(\kappa, 1)$ adds to $[T]$ a new element. Thus, if you just want to get the consistency of having a many large cardinals but for every weakly compact, $\kappa$, a $\kappa$-tree $T$ such that $2^{<\kappa}$ does not embed into it - you can start with a model with many large cardinals and add a single Cohen real. In the generic extension, $2^{<\kappa}$ is not a subtree of any ground model $\kappa$-tree, by Hamkin's Gap argument. | |
| Apr 17, 2016 at 13:58 | history | edited | Philipp Lücke | CC BY-SA 3.0 |
added 351 characters in body
|
| Apr 16, 2016 at 11:12 | history | edited | Philipp Lücke | CC BY-SA 3.0 |
added 116 characters in body
|
| Apr 15, 2016 at 18:55 | review | First posts | |||
| Apr 15, 2016 at 19:06 | |||||
| Apr 15, 2016 at 18:48 | history | answered | Philipp Lücke | CC BY-SA 3.0 |