Katarzyna W. Kowalik

activity

20202026

collaborators

4 papers

math.LO2026

Fraïssé's conjecture, partial impredicativity and well-ordering principles, part II

Anton Freund, Katarzyna W. Kowalik, Davide Manca

We exhibit a well-ordering principle that is equivalent to a theory of partial impredicativity. The latter goes back to Towsner and relates to recent work of Suzuki and Yokoyama. T…

math.LO2025

A non-speedup result for the chain-antichain principle over a weak base theory

Katarzyna W. Kowalik

We show that the theory $WKL_{0}^{*} + CAC$ is polynomially simulated by $RCA_{0}^{*}$ with respect to $\forall Π_{3}^{0}$ formulas. For the proof, we use the method of…

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 $CAC$ , the asc…

math.LO2020

How strong is Ramsey's theorem if infinity can be weak?

Leszek Aleksander Kołodziejczyk, Katarzyna W. Kowalik, Keita Yokoyama

We study the first-order consequences of Ramsey's Theorem for $k$ -colourings of $n$ -tuples, for fixed $n, k \geq 2$ , over the relatively weak second-order arithmetic theory $\mathrm…