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  1. Partition Genericity and Pigeonhole Basis Theorems.Benoit Monin & Ludovic Patey - 2024 - Journal of Symbolic Logic 89 (2):829-857.
    There exist two main notions of typicality in computability theory, namely, Cohen genericity and randomness. In this article, we introduce a new notion of genericity, called partition genericity, which is at the intersection of these two notions of typicality, and show that many basis theorems apply to partition genericity. More precisely, we prove that every co-hyperimmune set and every Kurtz random is partition generic, and that every partition generic set admits weak infinite subsets, for various notions of weakness. In particular, (...)
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