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On Lachlan’s major sub-degree problem
The Major Sub-degree Problem of A. H. Lachlan (first posed in 1967) has become a long-standing open question concerning the structure of the...
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Strong Enumeration Reducibilities
We investigate strong versions of enumeration reducibility, the most important one being s -reducibility. We prove that every countable distributive...
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The Medvedev lattice of computably closed sets
Simpson introduced the lattice
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The jump operation for structure degrees
One of the main problems in effective model theory is to find an appropriate information complexity measure of the algebraic structures in the sense...
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Approximation Representations for Δ2 Reals
We study Δ 2 reals x in terms of how they can be approximated symmetrically by a computable sequence of rationals. We deal with a natural notion of...
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Density of the Medvedev lattice of Π0 1 classes
The partial ordering of Medvedev reducibility restricted to the family of Π 0 1 classes is shown to be dense. For two disjoint computably enumerable...
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Isolation and the high/low hierarchy
Say that a d.c.e. degree d is isolated by a c.e. degree b , if b < d and any c.e. degree c below d is also below b , namely, b is the largest c.e....
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Post's problem for supertasks has both positive and negative solutions
The infinite time Turing machine analogue of Post's problem, the question whether there are semi-decidable supertask degrees between 0 and the...
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On the distribution of Lachlan nonsplitting bases
We say that a computably enumerable (c.e.) degree b is a Lachlan nonsplitting base (LNB) , if there is a computably enumerable degree a such that a > b ...
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Density results in the Δ20 e-degrees
We show that the Δ 0 2 enumeration degrees are dense. We also show that for every nonzero n -c. e. e-degree a , with n ≥ 3, one can always find a nonzero...
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On one-sided versus two-sided classification
One-sided classifiers are computable devices which read the characteristic function of a set and output a sequence of guesses which converges to 1...
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Index sets and parametric reductions
We investigate the index sets associated with the degree structures of computable sets under the parameterized reducibilities introduced by the...
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On the Quantitative Structure of Δ 2 0
We analyze the quantitative structure of Δ 2 0 . Among other things, we prove that a set is Turing...
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Computability in structures representing a Scott set
Continuing work begun in [10], we utilize a notion of forcing for which the generic objects are structures and which allows us to determine whether...