Complete coloring: Difference between revisions

From formulasearchengine
Jump to navigation Jump to search
← Older edit
en>Addbot
m Bot: Migrating 1 interwiki links, now provided by Wikidata on d:q3342988
en>David Eppstein
m authorlink Pavol Hell
 
Line 1: Line 1:
In [[mathematics]], and particularly in [[axiomatic set theory]], '''♣<sub>''S''</sub>''' ('''clubsuit''') is a family of [[Combinatorics|combinatorial principle]]s that are weaker version of the corresponding [[diamondsuit|◊<sub>''S''</sub>]]; it was introduced in 1975 <!--by A. Ostaszewski, but no article exists for him-->.
Glen Wendler is the title individuals use to call me and my spouse doesn't like it at all. Some time in the past she selected to live in [http://Statigr.am/tag/Delaware Delaware] but her husband wants them to transfer. Dispatching has been my profession for some time. Going to karaoke is some thing that I've carried out for many years. Go to my web site to discover out more: http://www.akasakarealestate.com/wiki/index.php/Nya_Internet_Svenska_Casino_P%C3%A5_N%C3%A4tet_-_The_Conspriracy<br><br>


== Definition ==
Also visit my web page: Närvarande hittar nya casinon villig nätet ([http://www.akasakarealestate.com/wiki/index.php/Nya_Internet_Svenska_Casino_P%C3%A5_N%C3%A4tet_-_The_Conspriracy Forslag Online-området])
 
For a given [[cardinal number]] <math>\kappa</math> and a [[stationary set]] <math>S \subseteq \kappa</math>, <math>\clubsuit_{S}</math> is the statement that there is a [[sequence]] <math>\left\langle A_\delta: \delta \in S\right\rangle</math> such that
 
* every ''A''<sub>''δ''</sub> is a cofinal [[subset]] of ''δ''
* for every [[Ordinal_number#Closed_unbounded_sets_and_classes|unbounded subset]] <math> A \subseteq \kappa</math>, there is a <math>\delta</math> so that <math>A_{\delta} \subseteq A</math>
<math>\clubsuit_{\omega_1}</math> is usually written as just <math>\clubsuit</math>.
 
== ♣ and ◊ ==
 
It is clear that ◊ ⇒ ♣, and it was shown in 1975 <!-- again by A. Ostaszewski--> that ♣ + [[continuum hypothesis|CH]] ⇒ ◊; however, [[Saharon Shelah]] gave a proof in 1980 that there exists a model of ♣ in which CH does not hold, so ♣ and ◊ are not equivalent (since ◊ ⇒ CH).
 
== References ==
 
* A. J. Ostaszewski, ''On countably compact perfectly [[normal space]]s'', Journal of [[London Mathematical Society]], 1975 (2) 14, pp. 505-516.
* S. Shelah, ''Whitehead groups may not be free, even assuming CH, II'', Israel Journal of Mathematics, 1980 (35) pp. 257-285.
 
== See also ==
*[[Club set]]
 
[[Category:Set theory]]

Latest revision as of 20:26, 13 May 2014

Glen Wendler is the title individuals use to call me and my spouse doesn't like it at all. Some time in the past she selected to live in Delaware but her husband wants them to transfer. Dispatching has been my profession for some time. Going to karaoke is some thing that I've carried out for many years. Go to my web site to discover out more: http://www.akasakarealestate.com/wiki/index.php/Nya_Internet_Svenska_Casino_P%C3%A5_N%C3%A4tet_-_The_Conspriracy

Also visit my web page: Närvarande hittar nya casinon villig nätet (Forslag Online-området)

Retrieved from "https://en.formulasearchengine.com/index.php?title=Complete_coloring&oldid=233518"