Definition
A subset A of the Baire space is universally Baire if it has one of the following equivalent properties:
- For every notion of forcing, there are trees T and U such that A is the projection of the set of all branches through T, and it is forced that the projections of the branches through T and the branches through U are complements of each other.
- For every compact Hausdorff space Ω, and every continuous function f from Ω to the Baire space, the preimage of A under f has the property of Baire in Ω.
- For every cardinal λ and every continuous function f from λω to the Baire space, the preimage of A under f has the property of Baire.
Read more about this topic: Universally Baire Set
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“Was man made stupid to see his own stupidity?
Is God by definition indifferent, beyond us all?
Is the eternal truth man’s fighting soul
Wherein the Beast ravens in its own avidity?”
—Richard Eberhart (b. 1904)
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—Adrienne Rich (b. 1929)