Lambda-Suslin

In mathematics, a subset "A" of κ^ω is λ-Suslin if there is a tree "T" on κ × λ such that "A" = p ["T" ] .

By a tree on κ × λ we mean here a subset "T" of the union of κ^"i" × λ^"i" for all "i" ∈ N (or "i" < ω in set-theoretical notation).

Here, p ["T" ] = { "f" | ∃"g" : ("f","g") ∈ ["T" ] } is the projection of "T",where ["T" ] = { ("f" , "g" ) | ∀"n" ∈ ω : ("f"("n"), "g"("n")) ∈ "T" } is the set of branches through "T".

Since ["T" ] is a closed set for the product topology on κ^ω × λ^ω (where κ and λ are equipped with the discrete topology) (and all closed sets in κ^ω × λ^ω come in this way from some tree on κ × λ), λ-Suslin subsets of κ^ω are projections of closed subsets in κ^ω × λ^ω.

When one talks of Suslin sets without specifying the space, then one usually means Suslin subsets of R, which graph theorists usually take to be the set ω^ω.

ee also

*Suslin cardinal

External links

* R. Ketchersid, [http://www.math.unt.edu/~ketchers/preprints/ideal.pdf The strength of an ω 1 -dense ideal on ω 1 under CH] , 2004.