Todd Eisworth
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Registered User
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Just your run-of-the-mill math professor/dad/set-theorist...
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May 15 |
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How far is Lindelöf from compactness? I wish I knew this result while Arhangelskii was still around our department. I could've answered lots of his questions! |
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May 10 |
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Question about Shelah’s version of “Shooting a club” found in PIF It won't be proper if $S$ is co-stationary (as the stationarity of the complement of $S$ is destroyed), but it will preserve $\omega_1$ because you get generics for "enough" elementary submodels. |
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May 10 |
accepted | Question about Shelah’s version of “Shooting a club” found in PIF |
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May 9 |
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Question about Shelah’s version of “Shooting a club” found in PIF Answered this quickly as I'm leaving work. If on the way home I realize I've said something silly, I'll edit! |
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May 9 |
answered | Question about Shelah’s version of “Shooting a club” found in PIF |
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Apr 16 |
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Examples of common false beliefs in mathematics. This error can be found in Gamow's famous book "One, Two, Three...Infinity", and even the Oxford English Dictionary contains a quote in their definition of "aleph null": "There is no infinite number between aleph-null (the number of positive integers) and aleph-one (the number of real numbers)." (apparently pulled from a Scientific American article) |
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Mar 14 |
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Is there in ZFC a topological space which is normal, ccc, countably compact, first countable and non-compact? Maybe it was Balogh. I know Fremlin and Nyikos were working on the problem as well, but that's all well before my time! |
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Mar 14 |
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Is there in ZFC a topological space which is normal, ccc, countably compact, first countable and non-compact? It's been a while since I've thought about these things, but I do have a couple of comments: In the work of mine you mention above, normality is a bit of a red herring as it is "perfect" and "regular" that allow us to build the notion of forcing needed for the proof to go through. It is also consistent with ZFC that every first countable, countably compact regular space is either compact or contains a homeomorphic copy of $\omega_1$. (I think that's originally due to Fremlin and Nyikos, but Peter Nyikos and I had a paper in the 2000s showing this consistent with CH as well.) |
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Feb 26 |
accepted | Why $z \in \overline{A}$? |
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Feb 26 |
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Why $z \in \overline{A}$? That is, you make sure $V_{i+1}\subseteq\overline{V}_{i+1}\subseteq V_i$, and then $\cap V_i = \cap \overline{V}_i$ is closed and a $G_\omega$ set. |
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Feb 26 |
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Why $z \in \overline{A}$? The nesting guarantees that the intersection of the V_i is the same as the intersection of their closures, hence closed. |
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Feb 26 |
awarded | ● Nice Answer |
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Feb 25 |
answered | Why $z \in \overline{A}$? |
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Jan 11 |
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Is there a (standard) name for $\bar{A}\setminus A$? I had a series of papers in set-theoretic topology where sets of this form were critical to analyzing a notion of forcing, and I never came across a standard name... |
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Dec 9 |
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Does a uniform space have a closed embedding in a product of metric spaces? Is the notion of "realcompact" what you are looking for? |
