Výsledky vyhledávání - "Khan, Mushfeq"

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From eventually different functions to pandemic numberings

Autor: Beros, Achilles A., Khan, Mushfeq, Kjos-Hanssen, Bjørn, Nies, André

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 such functions with varying growth bounds. In particular, there is no l

Externí odkaz: http://arxiv.org/abs/2002.01017

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Effective bi-immunity and randomness

Autor: Beros, Achilles A., Khan, Mushfeq, Kjos-Hanssen, Bjørn

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 relative to X that compute no ML random set. We show that the same holds w

Externí odkaz: http://arxiv.org/abs/1610.08615

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Forcing with Bushy Trees

Autor: Khan, Mushfeq, Miller, Joseph S.

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 noncomputable (DNC) functions that compute no Kurtz random real, as well as an e

Externí odkaz: http://arxiv.org/abs/1503.08870

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The Strength of the Gr\'atzer-Schmidt Theorem

Autor: Brodhead, Katie, Khan, Mushfeq, Kjos-Hanssen, Bjørn, Lampe, William A., Nguyen, Paul Kim Long V., Shore, Richard A.

Publikováno v: Archive for Mathematical Logic 55 (2016), no. 5, 687--704

The Gr\"atzer-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 theorem. We also show that the set of indices of computable lattices th

Externí odkaz: http://arxiv.org/abs/1408.2167

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