RAMSEY GROWTH IN SOME NIP STRUCTURES
RAMSEY GROWTH IN SOME NIP STRUCTURES
Abstract We investigate bounds in Ramseyā€™s theorem for relations definable in NIP structures. Applying model-theoretic methods to finitary combinatorics, we generalize a theorem of Bukh and Matousek ( Duke Mathematical Journal 163 (12) (2014), 2243ā€“2270) from the semialgebraic case to arbitrary polynomially bounded $o$ -minimal expansions of $\mathbb{R}$ , and ā€¦