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math.LO2015
Density-1-bounding and quasiminimality in the generic degrees
Peter Cholak, Gregory Igusa
We consider the question "Is every nonzero generic degree a density-1-bounding generic degree?" By previous results \cite{I2} either resolution of this question would answer an ope…
math.LO2015
Computable Ramsey's Theorem for Pairs Needs Infinitely Many Pi-0-2 Sets
Gregory Igusa, Henry Towsner
In \cite{J}, Theorem 4.2, Jockusch proves that for any computable k-coloring of pairs of integers, there is an infinite homogeneous set. The proof uses a countable collecti…
math.LO2015★ 2 cited
Any FIP real computes a 1-generic
Peter Cholak, Rod Downey, Greg Igusa
We construct a computable sequence of computable reals such that any real that can compute a subsequence that is maximal with respect to the finite intersectio…