In mathematical set theory, a square principle is a combinatorial principle asserting the existence of a cohering sequence of short closed unbounded (club) sets so that no one (long) club set coheres with them all. As such they may be viewed as a kind of incompactness phenomenon. They were introduced by Ronald Jensen in his analysis of the fine structure of the constructible universe L.

Definition

Define Sing to be the class of all limit ordinals which are not regular. Global square satisfying:

1. is a club set.

2. ot

\kappa-Suslin trees

is used to refine the construction.

Variant relative to a cardinal

Jensen introduced also a local version of the principle. satisfying:

1. is a club set.

.

Notes