ramsey’s theorem
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2021 ◽  
pp. 103028
Author(s):  
Marta Fiori-Carones ◽  
Leszek Aleksander Kołodziejczyk ◽  
Katarzyna W. Kowalik

2020 ◽  
Vol 369 ◽  
pp. 107180
Author(s):  
C.T. Chong ◽  
Wei Li ◽  
Wei Wang ◽  
Yue Yang

Computability ◽  
2020 ◽  
Vol 9 (2) ◽  
pp. 85-110
Author(s):  
Damir D. Dzhafarov ◽  
Jun Le Goh ◽  
Denis R. Hirschfeldt ◽  
Ludovic Patey ◽  
Arno Pauly

2019 ◽  
Vol 58 (7-8) ◽  
pp. 857-866 ◽  
Author(s):  
Jeffry L. Hirst ◽  
Carl Mummert

Author(s):  
Artem Chernikov ◽  
Sergei Starchenko ◽  
Margaret E. M. Thomas

We investigate bounds in Ramsey’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), 2243–2270) from the semialgebraic case to arbitrary polynomially bounded $o$ -minimal expansions of $\mathbb{R}$ , and show that it does not hold in $\mathbb{R}_{\exp }$ . This provides a new combinatorial characterization of polynomial boundedness for $o$ -minimal structures. We also prove an analog for relations definable in $P$ -minimal structures, in particular for the field of the $p$ -adics. Generalizing Conlon et al. (Transactions of the American Mathematical Society 366(9) (2014), 5043–5065), we show that in distal structures the upper bound for $k$ -ary definable relations is given by the exponential tower of height $k-1$ .


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