University Seminar- Computability, Complexity, and Algebraic Structure

Time: Wednesday, December 6, 11:15am – 12:15pm

Place: Monroe Hall, Room 250

Speaker: Philip White, GWU

Title:  An introduction to (κ, λ)-forests

Abstract: Given a cardinal κ, a κ-tree is a tree T of height κ where each node t in T is the meeting point of <κ many edges. A κ-branch is a subset S⊆T of order type κ that if t is in S then for all s<t we have s in S.  Koenig's Lemma is the well-known result that every ω-tree has an ω-branch.  Interestingly, there is a 2-cardinal analog of a κ-tree called a (κ, λ)-forest (sometimes called a mess), and instead of having κ-branches, a (κ, λ)-forest can have a (κ, λ)-grove.  Every κ-tree where κ is measurable has a κ-branch.  We will show that if κ is λ-supercompact then every (κ, λ)-forest has a (κ, λ)-grove.