Handbook of Set Theory

pp 93-128


Stationary Sets

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Stationary sets play a fundamental role in modern set theory. This chapter attempts to explain this role and to describe the structure of stationary sets of ordinals and their generalization.

In the first part we develop the theory of closed unbounded and stationary subsets of a regular uncountable cardinal. The closed unbounded sets generate the closed unbounded filter. The dual ideal is the nonstationary ideal.

Among properties of stationary sets discussed in the article are reflection and saturation. Both are closely related to large cardinal properties.

In the second part we consider the generalization from stationary sets of ordinals to stationary sets of models. These play an essential role in proper forcing, discussed elsewhere in the Handbook.