Global square

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Global square in an important concept in set theory, a branch of mathematics. Define Sing to be the class of all limit ordinals which are not regular. Global square states that there is a system (C_\beta)_{\beta \in Sing} satisfying:

  1. Cβ is a club set of β.
  2. ot(Cβ) < β
  3. If γ is a limit point of Cβ then \gamma \in Sing and C_\gamma = C_\beta \cap \gamma