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| '''Global square''' is an important concept in [[set theory]], a branch of [[mathematics]]. It has been introduced by [[Ronald Jensen]] in his analysis of the fine structure of the [[constructible universe]] '''L'''. According to
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| Ernest Schimmerling and Martin Zeman, ''Jensen's square principle and its variants are ubiquitous in set theory''.<ref>Ernest Schimmerling and Martin Zeman, Square in Core Models, The Bulletin of Symbolic Logic, Volume 7, Number 3, Sept. 2001</ref>
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| ==Definition==
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| Define '''Sing''' to be the [[class (set theory)|class]] of all [[limit ordinal]]s which are not [[regular ordinal|regular]]. ''Global square'' states that there is a system <math>(C_\beta)_{\beta \in Sing}</math> satisfying:
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| # <math>C_\beta</math> is a [[club set]] of <math>\beta</math>.
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| # [[order type|ot]]<math>(C_\beta) < \beta </math>
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| # If <math>\gamma</math> is a limit point of <math>C_\beta</math> then <math>\gamma \in Sing</math> and <math>C_\gamma = C_\beta \cap \gamma</math>
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| ==Variant relative to a cardinal==
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| Jensen introduced also a local version of the principle.<ref>{{Citation | last1=Jech | first1=Thomas | author1-link=Thomas Jech | title=Set Theory: Third Millennium Edition | publisher=[[Springer-Verlag]] | location=Berlin, New York | series=Springer Monographs in Mathematics | isbn=978-3-540-44085-7 | year=2003}}, p. 443.</ref> If
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| <math>\kappa</math> is an uncountable cardinal,
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| then <math>\Box_\kappa</math> asserts that there is a sequence <math>(C_\beta|\beta \text{ a limit point of }\kappa^+)</math> satisfying:
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| # <math>C_\beta</math> is a [[club set]] of <math>\beta</math>.
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| # If <math> cf \beta < \kappa </math>, then <math>|C_\beta| < \kappa </math>
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| # If <math>\gamma</math> is a limit point of <math>C_\beta</math> then <math>C_\gamma = C_\beta \cap \gamma</math>
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| ==Notes==
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| {{Reflist}}
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| [[Category:Set theory]]
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| {{settheory-stub}}
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The person who wrote the article is known as Jayson Hirano and he completely digs that name. To climb is something I really enjoy doing. For years she's been residing in Kentucky but her husband desires them to transfer. Office supervising is my profession.
Here is my web page - tarot card readings - www.prayerarmor.com,