1 ABSTRACT By generalizing to model theory notions connected with dimension, it is shown that certain theories categorical in uncountable powers have countably many de-numerable isomorphism types which are arranged in an ω + 1 sequence under the ordering of the possibility of elementary imbedding. It is also shown that any countable elementary extension of a denumerable saturated model of a the...

The edge tenacity Te(G) of a graph G is dened as:Te(G) = min {[|X|+τ(G-X)]/[ω(G-X)-1]|X ⊆ E(G) and ω(G-X) > 1} where the minimum is taken over every edge-cutset X that separates G into ω(G - X) components, and by τ(G - X) we denote the order of a largest component of G. The objective of this paper is to determine this quantity for split graphs. Let G = (Z; I; E) be a noncomplete connected split...

We consider reflexive Bergman spaces Ap(Ω) on polygonal domains Ω of the complex plane. With some restrictions to angles boundary Ω, we show that boundedness Toeplitz operator Tg:Ap(Ω)→Ap(Ω) with a positive symbol g is equivalent Berezin transform or times area measure being Carleson measure. The result also formulated for more general simply connected domains. main technical tool new weighted ...