Timeline for Is each Parovichenko compact space homeomorphic to the remainder of a soft compactification of $\mathbb N$?
Current License: CC BY-SA 4.0
12 events
| when toggle format | what | by | license | comment | |
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| Nov 14, 2018 at 8:44 | comment | added | KP Hart | Alan Dow's paper is open access: cms.math.ca/10.4153/CMB-1997-050-0 | |
| Nov 13, 2018 at 20:34 | comment | added | KP Hart | The application of (NT) to this example shows that it implies $\mathfrak{t}=\aleph_1$: the $L_\alpha$ determine a tower on $C_L$. Alan proved the consistency directly by iterated forcing (finite support, $\sigma$-centered). | |
| Nov 13, 2018 at 19:28 | comment | added | Taras Banakh | Thank you. Please correct $b\in \mathcal B$ to $B\in\mathcal B$ in the last but one line on page 4. You writes that (NT) is consistent with $\mathfrak c=\mathfrak b=\aleph_2$. Is it true that (NT) follows from $\mathfrak p>\aleph_1$? | |
| Nov 13, 2018 at 13:01 | comment | added | KP Hart | I have added the formulation to the note. | |
| Nov 12, 2018 at 23:27 | comment | added | Taras Banakh | Thank you. But It would be helpful to remind what does the principle (NT) says exactly. | |
| Nov 12, 2018 at 22:47 | comment | added | KP Hart | There is now a consistent counterexample, see the answer. | |
| Nov 12, 2018 at 22:46 | history | edited | KP Hart | CC BY-SA 4.0 |
Added mention of a counterexample.
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| Nov 9, 2018 at 22:37 | comment | added | KP Hart | All I can say about CH is that it appears to be needed in this proof: it needs countable initial segments and is the density of $X$ is equal to continuum then you expect to have to take care of continuum many pairs. The proof can be simplified a bit and I will do that later. | |
| Nov 9, 2018 at 17:30 | comment | added | Taras Banakh | Thank you for this partial solution. Indeed, the construction written in the pdf-file is rather complicated. Is it indeed requires the full strenth of CH, or something weaker like $\mathfrak t=\mathfrak c$? | |
| Nov 9, 2018 at 17:28 | vote | accept | Taras Banakh | ||
| Nov 9, 2018 at 13:57 | history | edited | KP Hart | CC BY-SA 4.0 |
added 1 character in body
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| Nov 9, 2018 at 12:59 | history | answered | KP Hart | CC BY-SA 4.0 |