ANY FIP REAL COMPUTES A 1-GENERIC

作者:Cholak Peter*; Downey Rodney G; Igusa Greg
来源:Transactions of the American Mathematical Society, 2017, 369(8): 5855-5869.
DOI:10.1090/tran/6997

摘要

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. 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.

  • 出版日期2017-8

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