The object of the investigation is to study reducible $M$-ideals in Banach spaces. It is shown that if the number of $M$-ideals in a Banach space $X$ is $n(<infty)$, then the number of reducible $M$-ideals does not exceed of $frac{(n-2)(n-3)}{2}$. Moreover, given a compact metric space $X$, we obtain a general form of a reducible $M$-ideal in the space $C(X)$ of continuous functions on $X$. The...

Under Martin’s Maximum every σ-ideal on ω1 is a subset of an ideal Rudin-Keisler reducible to a finite Fubini power of the nonstationary ideal restricted to a positive set.

We are mainly concerned with the completablity of unimodular rows to an invertible matrix. We first relate this to stable range of the ring. Further, we consider rows generating an idempotent of the ring to obtain completability under special conditions. We try to obtain analogues of important theorems regarding unimodular rows in the case of these “idempotent rows”. By ring, we shall always me...

A partial information algorithm for a language A computes, for some fixed m, for input words x1, . . . , xm a set of bitstrings containing χA(x1, . . . , xm). E.g., p-selective, approximable, and easily countable languages are defined by the existence of polynomial-time partial information algorithms of specific type. Self-reducible languages, for different types of self-reductions, form subcla...

Let M be a simple 3-manifold with F a component of ∂M of genus at least two. For a slope α on F , we denote by M(α) the manifold obtained by attaching a 2-handle to M along a regular neighborhood of α on F . Suppose that α and β are two separating slopes on F such that M(α) and M(β) are reducible. Then the distance between α and β is at most 2. As a corollary, if g(F ) = 2, then there is at mos...

It is proved that if A is aregular uniform algebra on a compact Hausdorff space X in which every closed ideal is an M-ideal, then A = C(X).

We recall from [10] a Gδ σ-ideal of compact subsets of 2 ω and prove that it is not Tukey reducible to the ideal I1/n = {H ⊆ ω : ∑ h∈H 1/h <∞}. This result answers a question of S. Solecki and S. Todorčević in the negative.

A set A is m-reducible (or Karp-reducible) to B if and only if there is a polynomial-time computable function f such that, for all x, x ∈ A if and only if f(x) ∈ B. Two sets are: • 1-equivalent if and only if each is m-reducible to the other by one-one reductions; • p-invertible equivalent if and only if each is m-reducible to the other by one-one, polynomial-time invertible reductions; and • p...

Let (M ;⊆) and (L ;⊆) be the lattices of additive induced-hereditary properties of graphs and additive hereditary properties of graphs, respectively. A property R∈Ma (∈ L) is called a minimal reducible bound for a property P∈Ma (∈ L) if in the interval (P;R) of the lattice M (L) there are only irreducible properties. The set of all minimal reducible bounds of a property P∈Ma in the lattice M we...