Canonical immunity and genericity
Volume 254 / 2021
Fundamenta Mathematicae 254 (2021), 241-259 MSC: 03D28, 68Q30. DOI: 10.4064/fm11-2-2021 Published online: 12 April 2021
Whereas the usual notions of immunity—e.g., immunity, hyperimmunity, etc.—are associated with Cohen genericity, canonical immunity (introduced by Beros–Khan–Kjos-Hanssen (2017)) is associated instead with Mathias genericity. Specifically, every Mathias generic is canonically immune and no Cohen 2-generic computes a canonically immune set.