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math.LO2022
Carlson-Simpson's lemma and applications in reverse mathematics
Paul-Elliot Anglès d'Auriac, Bastien Mignoty, Lu Liu +1
We study the reverse mathematics of infinitary extensions of the Hales-Jewett theorem, due to Carlson and Simpson. These theorems have multiple applications in Ramsey's theory, suc…
math.LO2022
The Reverse Mathematics of CAC for trees
Julien Cervelle, William Gaudelier, Ludovic Patey
CAC for trees is the statement asserting that any infinite subtree of has an infinite path or an infinite antichain. In this paper, we study the computat…
math.LO2022★ 2 cited
Partition genericity and pigeonhole basis theorems
Benoit Monin, Ludovic Patey
There exist two notions of typicality in computability theory, namely, genericity and randomness. In this article, we introduce a new notion of genericity, called partition generic…