Any FIP real computes a 1-generic

2015/02/12 by Peter Cholak, Cholak, Peter, Rodney G. Downey +3 · 1 citation
Computer Science · Mathematics · #03D30 #Advanced Topology and Set Theory #Computability, Logic, AI Algorithms #FOS: Mathematics #Logic (math.LO) #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.1502.03785

openalex publication_date 2015/02/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We construct a computable sequence of computable reals ⟨ X_i⟩ such that any real that can compute a subsequence that is maximal with respect to the finite intersection property can also compute a Cohen 1-generic. This is extended to establish the same result with 2IP in place of FIP.

Cited by

• Iterated jump noncomputability and compactness

Related

• Combinatorial and number-theoretic properties of generic reals
• Cohen-like first order structures
• Adding a lot of Cohen reals by adding a few
• Adding ℵ_ω many Cohen reals
• Computable one-way functions on the reals