Infinitary Combinatorics and Finitary Arithmetic

Explore recent developments in reverse mathematics and the characterization of Ramsey-type combinatorial principles in this hour-long conference talk. Delve into the framework of reverse mathematics, which analyzes and calibrates the proof-theoretic strength of mathematical theorems. Learn how mathematical theorems are expressed in first or second-order language of arithmetic and how the class of sentences provable by a theorem over a base system is characterized. Gain insights into the latest advancements in the characterization problem of specific Ramsey-type combinatorial principles, bridging the gap between infinitary combinatorics and finitary arithmetic.