In the presence of suitable power spaces, compactness ofX can be characterized as the singleton {∅} being open in the space A(X). Equivalently, this means that universal quantification over a compact space preserves open predicates. Using the language of represented spaces, one can make sense of notions such as a Σ 2 subset of the space of Σ 2 -subsets of a given space. This suggests higher-ord...

Noetherian spaces are a topological concept that generalizes well quasiorderings. We explore applications to infinite-state verification problems, and show how this stimulated the search for infinite procedures à la Karp-Miller.

Recently N. Nitsure showed that for a coherent sheaf F on a noetherian scheme the automorphism functor AutF is representable if and only if F is locally free. Here we remove the noetherian hypothesis and show that the same result holds for the endomorphism functor EndF even if one asks for representability by an algebraic space.

In this paper all coordinates in two variables over a Noetherian Q-domain of Krull dimension one are proved to be projectively tame. In order to do this, some results concerning projectively-tameness of polynomials in general are shown. Furthermore, we deduce that all automorphisms in two variables over a Noetherian reduced ring of dimension zero are tame.

We show that the space of transfinite words, is, ordinal-indexed over a Noetherian is also Noetherian, under natural topology which we call regular subword topology. characterize its sobrification and specialization ordering

For every variety of algebras Θ and every algebra H ∈ Θ we can consider an algebraic geometry in Θ over H. Algebras in Θ may be many sorted (not necessarily one sorted) algebras. A set of sorts Γ is fixed for each Θ. This theory can be applied to the variety of representations of groups over fixed commutative ring K with unit. We consider a representation as two sorted algebra (V, G), where V i...

In the paper we prove (Theorem 8.1) that there exists a continuum of non isomorphic simple modules over KF 2 , where F 2 is a free group with 2 generators (compare with [Ca] where a continuum of non isomorphic simple 2-generated groups is constructed). Using this fact we give an example of a non action type logically Noetherian representation (Section 9). In general, the topic of this paper is ...

In this paper we look at the properties of modules and prime ideals in finite dimensional noetherian rings. This paper is divided into four sections. The first section deals with noetherian one-dimensional rings. Section Two deals with what we define a “zero minimum rings” and explores necessary and sufficient conditions for the property to hold. In Section Three, we come to the minimal prime i...