Any FIP real computes a 1-generic

We construct a computable sequence of computable reals \langle X_i\rangle 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. Thi...

Full description

Saved in:
Bibliographic Details
Published in:Transactions of the American Mathematical Society 2017-08, Vol.369 (8), p.5855-5869
Main Authors: CHOLAK, PETER, DOWNEY, RODNEY G., IGUSA, GREG
Format: Article
Language:English
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:We construct a computable sequence of computable reals \langle X_i\rangle 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. This is the first example of a classical theorem of mathematics that has been found to be equivalent, both proof theoretically and in terms of its effective content, to computing a 1-generic.
ISSN:0002-9947
1088-6850
DOI:10.1090/tran/6997