1 citations · 2 across the 3 of their papers we have counts for
4 papers
From eventually different functions to pandemic numberings
Achilles A. Beros, Mushfeq Khan, Bjørn Kjos-Hanssen +1
A function is strongly non-recursive (SNR) if it is eventually different from each recursive function. We obtain hierarchy results for the mass problems associated with computing s…
Effective bi-immunity and randomness
Achilles A. Beros, Mushfeq Khan, Bjørn Kjos-Hanssen
We study the relationship between randomness and effective bi-immunity. Greenberg and Miller have shown that for any oracle X, there are arbitrarily slow-growing DNR functions rela…
Forcing with Bushy Trees
Mushfeq Khan, Joseph S. Miller
We present several results that rely on arguments involving the combinatorics of "bushy trees". These include the fact that there are arbitrarily slow-growing diagonally noncomputa…
The Strength of the Grätzer-Schmidt Theorem
Katie Brodhead, Mushfeq Khan, Bjørn Kjos-Hanssen +3
The Grätzer-Schmidt theorem of lattice theory states that each algebraic lattice is isomorphic to the congruence lattice of an algebra. We study the reverse mathematics of this the…