Logic Seminar
Finiteness classes arising from Ramsey-theoretic statements in set theory without choice
We investigate infinite sets that witness the failure of certain Ramsey-theoretic statements, such as Ramsey's or (appropriately phrased) Hindman's theorem; such sets may exist if one does not assume the Axiom of Choice. We will show very precise information as to where such sets are located within the hierarchy of infinite Dedekind-finite sets. The proofs involve both very pleasant combinatorial arguments (to establish certain implications) and the Fränkel-Mostowski technique to obtain permutation models of ZFA (to prove that certain other implications are not provable). Speaker(s): Joshua, Mengyang, David; Brot, Cao, Fernandez-Breton, respectively (University of Michigan)
Building: | East Hall |
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Event Type: | Workshop / Seminar |
Tags: | Mathematics |
Source: | Happening @ Michigan from Department of Mathematics, Logic Seminar - Department of Mathematics |