Title：Indiscernible Subsequence in NIP Theories

Speaker：Chuyin Jiang (UCLA)

Time: 2024/10/30 11:00-12:00

Zoom room: 717 463 6082

Organizer: Kyle Gannon (BICMR)

Abstract：

　　Ramsey's theorem, which establishes the existence of monochromatic cliques in edge-colored complete graphs, forms the foundation of Ramsey theory, a field dedicated to uncovering patterns within seemingly disordered structures. As the scope of the problem expands to include multiple colorings, hypergraphs, and infinite sets, the existence of Ramsey cardinals cannot be established within ZFC. In this presentation, we reinterpret n-types as colorings of ordered sequences, where a "monochromatic clique" corresponds to an indiscernible subsequence. We will discuss the implications of this framework for the existence of Ramsey cardinals in NIP theories.