Math 2.0

Mathematical logic and foundations Ordinals and cardinals Concept

Club set

Summary

A club set is a subset of a limit ordinal that is closed under limits and unbounded, and the name abbreviates "closed unbounded". Below a regular cardinal κ>ω\kappa > \omega, the club sets play the role of "large" sets: the intersection of fewer than κ\kappa of them is again club. They define the stationary sets, and the precise definition is given separately.

Further reading

  1. Web https://en.wikipedia.org/wiki/Club_set
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Changed2 November 2026

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