GO-spaces and Noetherian spectra

Go-spaces and Noetherian Spectra

The Noetherian type of a space is the least κ for which the space has a κop-like base, i.e., a base in which no element has κ-many supersets. We prove some results about Noetherian types of (generalized) ordered spaces and products thereof. For example: the density of a product of not-too-many compact linear orders never exceeds its Noetherian type, with equality possible only for singular Noet...

Noetherian Quasi-Polish spaces

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 in Verification

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.

Reverse mathematics, well-quasi-orders, and Noetherian spaces

Finite Correspondence of Spectra in Noetherian Ring Extensions

Let R <-* S be an embedding of associative noetherian rings such that 5 is finitely generated as a right Ä-module. There is a correspondence from the prime spectrum of S to the prime spectrum of R obtained by associating to a given prime ideal P of S the prime ideals of R minimal over P n R . The prime and primitive ideal theories for several specific noncommutative noetherian rings, including ...