The finite intersection principle and genericity
David Diamondstone, Rodney G. Downey, Noam Greenberg, Dan Turetsky · Mathematical Proceedings of the Cambridge Philosophical Society · 2015
Abstract We show that a Δ02 Turing degree computes solutions to all computable instances of the finite intersection principle if and only if it computes a 1-generic degree. We also investigate finite and infinite variants of the principle.