In a countable superstable NDOP theory, the existence of a rigid אǫ-saturated model implies the existence of 2 λ rigid אǫ-saturated models of power λ for every λ > 2א0 .

In this paper, we prove the number of countable models of a countable supersimple theory is either 1 or infinite. This result is an extension of Lachlan’s theorem on a superstable theory.

Silvers’s perfect set theorem says that every Π1 equivalence relation over a polish space either has countably many equivalence classes or has a perfect set of inequivalent elements. We prove an analog where the equivalence relation is replaced by a Π1 dependence relation, and the perfect set of inequivalent elements is replaced by a perfect independent set. The dependence relation should satis...

In a countable superstable NDOP theory, the existence of a rigid א2-saturated model implies the existence of 2 λ rigid א2-saturated models of power λ for every λ > 2א0 .

We prove that if $G=(V,E)$ is an $\omega$-stable (respectively, superstable) graph with $\chi (G)>\aleph _0$ $2^{\aleph _0}$) then $G$ contains all the finite subgraphs of shift $\mathrm {Sh}_n(\omega )$ for some $n$. a variant this theorem graphs interpretable in stationary stable theories. Furthermore, $\operatorname {U}(G)\leq 2$ we $n\leq suffices.

A first-order theory T has the Schröder-Bernstein (SB) property if any pair of elementarily bi-embeddable models are isomorphic. We prove that T has an expansion by constants that has the SB property if and only if T is superstable and non-multidimensional. We also prove that among superstable theories T , the class of a-saturated models of T has the SB property if and only if T has no nomadic ...

the aim of this paper is to show that under some mild conditions a functional equation of multiplicative (; )-derivation is superstable on standard operator algebras. furthermore, we prove that this generalized derivation can be a continuous and an inner (; )- derivation.