Ordinal determinacy

AD+

In set theory, AD+ is an extension, proposed by W. Hugh Woodin, to the axiom of determinacy. The axiom, which is to be understood in the context of ZF plus DCR (the axiom of dependent choice for reals), states two things:

  1. Every set of reals is ∞-Borel.
  2. For any ordinal λ less than Θ, any subset A of ωω, and any continuous function π:λω→ωω, the preimage π-1[A] is determined. (Here λω is to be given the product topology, starting with the discrete topology on λ.)

The second clause by itself is called ordinal determinacy.

External links

Search another word or see Ordinal determinacyon Dictionary | Thesaurus |Spanish
Copyright © 2014 Dictionary.com, LLC. All rights reserved.
  • Please Login or Sign Up to use the Recent Searches feature