Square principle

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In mathematical set theory, the global square principle is a combinatorial principle introduced by Ronald Jensen in his analysis of the fine structure of the constructible universe L.


Define Sing to be the class of all limit ordinals which are not regular. Global square states that there is a system satisfying:

  1. is a club set of .
  2. ot
  3. If is a limit point of then and

Variant relative to a cardinal[edit]

Jensen introduced also a local version of the principle.[1] If is an uncountable cardinal, then asserts that there is a sequence satisfying:

  1. is a club set of .
  2. If , then
  3. If is a limit point of then

Jensen proved that this principle holds in the constructible universe for any uncountable cardinal κ.


  1. ^ Jech, Thomas (2003), Set Theory: Third Millennium Edition, Springer Monographs in Mathematics, Berlin, New York: Springer-Verlag, ISBN 978-3-540-44085-7 , p. 443.