We prove that every countable jump upper semilattice can be embedded in D, where a jump upper semilattice (jusl) is an upper semilattice endowed with a strictly increasing and monotone unary operator… (More)

We show that the theory of D(6 g), where g is a 2-generic or a 1-generic degree below 0′, interprets true first order arithmetic. To this end we show that 1-genericity is sufficient to find the… (More)

We study the classes of Buchi and Rabin automatic structures. For Buchi (Rabin) automatic structures their domains consist of infinite strings (trees), and the basic relations, including the equality… (More)

We prove that there is a structure, indeed a linear ordering, whose degree spectrum is the set of all non-hyperarithmetic degrees. We also show that degree spectra can distinguish measure from… (More)

We prove that the isomorphism problem for torsion-free Abelian groups is as complicated as any isomorphism problem could be in terms of the analytical hierarchy, namely Σ1 complete.

We prove that the existential theory of the Turing degrees, in the language with Turing reduction, 0, and unary relations for the classes in the generalized high/low hierarchy, is decidable.

A statement of hyperarithmetic analysis is a sentence of second order arithmetic S such that for every Y ⊆ ω, the minimum ω-model containing Y of RCA0+S is HYP(Y), the ω-model consisting of the sets… (More)

The goal of this paper is to construct a computable א0-categorical structure whose first order theory is computably equivalent to the true first order theory of arithmetic. Recall that a structure is… (More)

In [RS07, RS08], Reimann and Slaman raise the question “For which infinite binary sequences X do there exist continuous probability measures μ such that X is effectively random relative to μ?”. They… (More)