Timeline for A problem of Keisler and Tarski
Current License: CC BY-SA 3.0
10 events
| when toggle format | what | by | license | comment | |
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| Jan 10, 2016 at 21:18 | answer | added | Boaz Tsaban | timeline score: 1 | |
| Sep 18, 2015 at 11:37 | comment | added | Avshalom | There is a 1993 survey paper by Grzegorz Plebanek in FM; section 6 is the relevant bit perhaps: matwbn.icm.edu.pl/ksiazki/fm/fm143/fm14312.pdf | |
| Sep 18, 2015 at 10:34 | history | edited | Emil Jeřábek | CC BY-SA 3.0 |
fix name
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| Sep 18, 2015 at 6:30 | comment | added | Mohammad Golshani | $\to$ The authors show that the equality persists for higher versions of these cardinals, where one replaces "countable'' by "smaller than $κ$''' in the definitions. Call $κ$ submeasurable if there is a nonzero diffuse and $κ$-continuous submeasure on $P(κ)$, where $κ$-continuous means "continuous for nets of size less than $κ$''. | |
| Sep 18, 2015 at 6:29 | comment | added | Mohammad Golshani | $\to$ The first cardinals of each type are all equal and weakly inaccessible but not larger than the first real-valued measurable cardinal (equality is still an open problem). | |
| Sep 18, 2015 at 6:28 | comment | added | Mohammad Golshani | $\to$ finally a $g$-sequential cardinal is a $κ$ such that $Z^κ$ admits a sequentially continuous but not continuous homomorphism or, equivalently, $P(κ)$ admits a diffuse sequentially continuous submeasure | |
| Sep 18, 2015 at 6:27 | comment | added | Mohammad Golshani | A related paper might be "Sequential continuity and submeasurable cardinals" by Balcar and Hušek. The following is taken from the review of their paper from Mathscinet: The relationship between continuity and sequential continuity is, outside the class of sequential spaces, decidely one-sided. An exception can be made for the Cantor cubes $2^κ$; call a cardinal $κ$ sequential if $2^κ$ admits a real-valued function that is sequentially continuous but not continuous; call $κ$ uniformly sequential if $2^κ$ admits a real-valued function that is sequentially uniformly continuous but not continuous. | |
| S Sep 18, 2015 at 2:00 | history | suggested | CommunityBot | CC BY-SA 3.0 |
Added italics to journal names, as per the usual academic standards.
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| Sep 18, 2015 at 1:28 | review | Suggested edits | |||
| S Sep 18, 2015 at 2:00 | |||||
| Sep 18, 2015 at 0:22 | history | asked | Ashutosh | CC BY-SA 3.0 |