3 papers
math.LO2021
Weaker cousins of Ramsey's theorem over a weak base theory
Marta Fiori-Carones, Leszek Aleksander Kołodziejczyk, Katarzyna W. Kowalik
The paper is devoted to a reverse-mathematical study of some well-known consequences of Ramsey's theorem for pairs, focused on the chain-antichain principle , the asc…
math.LO2020
Ramsey's theorem for pairs, collection, and proof size
Leszek Aleksander Kołodziejczyk, Tin Lok Wong, Keita Yokoyama
We prove that any proof of a sentence in the theory can be translated into a proof in at the cost of a polynomia…
math.CO2018
Some upper bounds on ordinal-valued Ramsey numbers for colourings of pairs
Leszek Aleksander Kołodziejczyk, Keita Yokoyama
We study Ramsey's theorem for pairs and two colours in the context of the theory of -large sets introduced by Ketonen and Solovay. We prove that any -colouring of pairs from…