4 citations · 9 across the 6 of their papers we have counts for
6 papers · 1 filter
Primitive recursive reverse mathematics
Nikolay Bazhenov, Marta Fiori-Carones, Lu Liu +1
We use a second-order analogy of to investigate the proof-theoretic strength of theorems in countable algebra, analysis, and infinite combinatorics.…
An isomorphism theorem for models of Weak König's Lemma without primitive recursion
Marta Fiori-Carones, Leszek Aleksander Kołodziejczyk, Tin Lok Wong +1
We prove that if and are countable models of the theory such that fails for some $A \in \mathcal{X} \cap \…
(Extra)ordinary equivalences with the ascending/descending sequence principle
Marta Fiori-Carones, Alberto Marcone, Paul Shafer +1
We analyze the axiomatic strength of the following theorem due to Rival and Sands in the style of reverse mathematics. "Every infinite partial order of finite width contains an…
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…
An inside/outside Ramsey theorem and recursion theory
Marta Fiori-Carones, Paul Shafer, Giovanni Soldà
Inspired by Ramsey's theorem for pairs, Rival and Sands proved what we refer to as an inside/outside Ramsey theorem: every infinite graph contains an infinite subset such t…
To reorient is easier than to orient: an on-line algorithm for reorientation of graphs
Marta Fiori-Carones, Alberto Marcone
We define an on-line (incremental) algorithm that, given a (possibly infinite) pseudo-transitive oriented graph, produces a transitive reorientation. This implies that a theorem of…