Introduction. According to a classical theorem of Post, the arithmetical sets may be obtained by the following construction : Step 0: "take" all the r.e. sets. Step n+1 : "add" all sets which are r.e. in sets "taken" at a previous stage. Moreover, this construction is intimately related to the Kleene arithmetical hierarchy, defined in terms of the number and quality of alternating numberquantif...

A set $S subseteq V(G)$ is a semitotal dominating set of a graph $G$ if it is a dominating set of $G$ andevery vertex in $S$ is within distance 2 of another vertex of $S$. Thesemitotal domination number $gamma_{t2}(G)$ is the minimumcardinality of a semitotal dominating set of $G$.We show that the semitotal domination problem isAPX-complete for bounded-degree graphs, and the semitotal dominatio...

Π1 classes are important to the logical analysis of many parts of mathematics. The Π1 classes form a lattice. As with the lattice of computably enumerable sets, it is natural to explore the relationship between this lattice and the Turing degrees. We focus on an analog of maximality, or more precisely, hyperhypersimplicity, namely the notion of a thin class. We prove a number of results relatin...

A computably enumerable (c.e.) degree is a maximal contiguous degree if it is contiguous and no c.e. degree strictly above it is contiguous. We show that there are infinitely many maximal contiguous degrees. Since the contiguous degrees are definable, the class of maximal contiguous degrees provides the first example of a definable infinite anti-chain in the c.e. degrees. In addition, we show t...

In Chapter I, we exhibit a high strongly noncappable degree. Chapter II answers negatively the question whether a deep degree exists. It also shows a weak converse of this. Chapter III is devoted to index sets. We define a family of properties on hyperhypersimple sets and show that they yield index sets at each level of the hyperarithmetical hierarchy. We also classify the index set of quasimax...

We study, in three parts, degree sequences of k-families (or k-uniform hypergraphs) and shifted k-families. • The first part collects for the first time in one place, various implications such as Threshold ⇒ Uniquely Realizable ⇒ Degree-Maximal ⇒ Shifted which are equivalent concepts for 2-families (= simple graphs), but strict implications for kfamilies with k ≥ 3. The implication that uniquel...

Let (X, ®, m) be a Lebesgue space, m(X) = 1, and let T be an invertible measurable nonsingular aperiodic transformation of X onto X. If S is a set of r integers, r > 2, then there exists a set A of measure less than /•"' S*_! k~l such that X = U,es T"A. Thus for every infinite set of integers W there exist sets A of arbitrarily small measure such that X = U nniv T"A.

three iranian native strains and three japanese commercial lines of the silkworm bombyx mori were analyzed using amplified fragment length polymorphism (aflp) markers. a set of ten psti/taqi primer combinations amplified a total of 322 bands out of which 251 (%78) were polymorphic. estimates of nei’s gene diversity for all loci in individual strains and commercial lines indicated a higher degre...

0 1 classes are important to the logical analysis of many parts of mathematics. The 0 1 classes form a lattice. As with the lattice of computable enumerable sets, it is natural to explore the relationship between this lattice and the Turing degrees. We focus on an analog of maximality namely the notion of a thin class. We prove a number of results relating automorphisms, invariance and thin cla...