Complete coloring - Revision history

en>David Eppstein: authorlink Pavol Hell

2014-05-13T18:26:33Z

← Older revision		Revision as of 20:26, 13 May 2014
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	~~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]]~~

en>Addbot: Bot: Migrating 1 interwiki links, now provided by Wikidata on d:q3342988

2013-03-13T08:11:58Z

Bot: Migrating 1 interwiki links, now provided by Wikidata on d:q3342988

← Older revision		Revision as of 10:11, 13 March 2013
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	~~The author~~ is ~~known as Irwin Wunder but it'~~s ~~not~~ the ~~most masucline title out there~~. For ~~years I~~'~~ve been operating~~ as ~~a payroll clerk~~. ~~Her spouse~~ and ~~her live in Puerto Rico but she will have to transfer one day or an additional. Body developing~~ is ~~what my family members~~ and ~~I enjoy~~.~~<br~~>~~<br>Look at my site~~ ... [~~http://ece~~.~~modares~~.ac.~~ir/mnl/?q=node/967954 modares~~.ac.ir]		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-->.

			== Definition ==

			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]]

en>David Eppstein: /* Special classes of graphs */ authorlink Hans L. Bodlaender

2012-02-18T22:22:09Z

Special classes of graphs: authorlink Hans L. Bodlaender

New page

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