# Stationary Set

In mathematics, particularly in set theory and model theory, there are at least three notions of stationary set:

### Other articles related to "set, stationary, stationary set":

Minimal Condition Sufficient For A Mahlo Cardinal
... If κ is a limit ordinal and the set of regular ordinals less than κ is stationary in κ, then κ is weakly Mahlo ... suppose that it is not regular and construct a club set which gives us a μ such that μ = cf(μ) < cf(κ) < μ < κ which is a contradiction ... No stationary set can exist below with the required property because {2,3,4...} is club in ω but contains no regular ordinals so κ is uncountable ...
Stationary Set - Generalized Notion
... Now let be a nonempty set ... A set is club (closed and unbounded) if and only if there is a function such that ... is stationary in if and only if it meets every club subset of ...

### Famous quotes containing the words set and/or stationary:

Well, most men have bound their eyes with one or another handkerchief, and attached themselves to some of these communities of opinion. This conformity makes them not false in a few particulars, authors of a few lies, but false in all particulars. Their every truth is not quite true. Their two is not the real two, their four not the real four; so that every word they say chagrins us and we know not where to set them right.
Ralph Waldo Emerson (1803–1882)

It is the dissenter, the theorist, the aspirant, who is quitting this ancient domain to embark on seas of adventure, who engages our interest. Omitting then for the present all notice of the stationary class, we shall find that the movement party divides itself into two classes, the actors, and the students.
Ralph Waldo Emerson (1803–1882)