2 citations · 4 across the 7 of their papers we have counts for
8 papers
The Rado Path Decomposition Theorem
Peter Cholak, Gregory Igusa, Ludovic Patey +2
We discuss a theorem of Rado: Every r-coloring of the pairs of natural numbers has a path decomposition.
Some new computable structures of high rank
Matthew Harrison-Trainor, Gregory Igusa, Julia F. Knight
We give several new examples of computable structures of high Scott rank. For earlier known computable structures of Scott rank , the computable infinitary theory is $\al…
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…
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…
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…
Notions of robust information coding
Damir Dzhafarov, Gregory Igusa
We introduce and study several notions of computability-theoretic reducibility between subsets of that are "robust" in the sense that if only partial information is available a…