We prove the following three theorems on the enumeration degrees of Σ2 sets. Theorem A: There exists a nonzero noncuppable Σ 0 2 enumeration degree. Theorem B: Every nonzero ∆2 enumeration degree is cuppable to 0e by an incomplete total enumeration degree. Theorem C: There exists a nonzero low ∆2 enumeration degree with the anticupping property.

We present an open-geometry Fourier modal method based on a new combination of open boundary conditions and an efficient k-space discretization. The open boundary of the computational domain is obtained using basis functions that expand the whole space, and the integrals subsequently appearing due to the continuous nature of the radiation modes are handled using a discretization based on nonuni...

We ask when certain complete intersections of codimension r can lie on a generic hypersurface in Pn. We give a complete answer to this question when 2r ≤ n + 2 in terms of the degrees of the hypersurfaces and of the degrees of the generators of the complete intersection.

It is proven that there is a family of sets of natural numbers which has enumerations in every Turing degree except for the recursive degree. This implies that there is a countable structure which has representations in all but the recursive degree. Moreover, it is shown that there is such a structure which has a recursively represented elementary extension.

For every finitely generated recursively presented group G we construct a finitely presented group H containing G such that G is (Frattini) embedded into H and the group H has solvable conjugacy problem if and only if G has solvable conjugacy problem. Moreover G and H have the same r.e. Turing degrees of the conjugacy problem. This solves a problem by D. Collins.

We define the automorphism spectrum of a computable structure M, a measurement of the complexity of the symmetries of M, and prove that certain sets of Turing degrees can be realized as automorphism spectra, while certain others cannot.

Much of the work on Turing degrees may be formulated in terms of the embeddability of certain first-order structures in a structure whose universe is some set of degrees and whose relations, functions, and constants are natural degree-theoretic ones. Thus, for example, we know that if (P, ≤P ) is a partial ordering of cardinality at most א1 which is locally countable—each point has at most coun...

This paper carefully follows graduates of the largest of Israel's public colleges, their success in their studies at the College, and in their studies towards graduate degrees in institutions of higher education in Israel. It explores who these graduates are, where they came from, their academic success, and where they headed after attaining an undergraduate degree. The aim is to examine the li...

We propose a meta-theorem from which some splitting theorem for total e-degrees can be derived.

For every finitely generated recursively presented group G we construct a finitely presented group H containing G such that G is (Frattini) embedded into H and the group H has solvable conjugacy problem if and only if G has solvable conjugacy problem. Moreover, G and H have the same r.e. Turing degrees of the conjugacy problem. This solves a problem by D.