Jing Zhang: A polarized partition theorem for large saturated linear orders

Mathematical logic seminar – Mar 28 2017
Time:     3:30pm – 4:30 pm

Room:     Wean Hall 8220

Speaker:         Jing Zhang
Department of Mathematical Sciences
CMU

Title:     A polarized partition theorem for large saturated linear orders

Abstract:     Laver proved the following polarized partition theorem for rational numbers: for any natural number d, any finite coloring f of Q^d, there exist subsets of Q, X_i for i < d, each of which has the same order type as Q such that the product X_1 x … x X_{d-1} gets at most d! many colors. A natural question to ask is what happens when we consider larger saturated linear orders. We will discuss the consistency at the level of strongly inaccessible cardinals that satisfy some indestructibility property. The development of versions of the Halpern-Läuchli theorem at a large cardinal will be pivotal in the proof.

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