Noetherian loop spaces

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.

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...

The Dynamical Mordell-lang Problem for Noetherian Spaces

Let X be a Noetherian space, let Φ : X −→ X be a continuous function, let Y ⊆ X be a closed set, and let x ∈ X. We show that the set S := {n ∈ N : Φn(x) ∈ Y } is a union of at most finitely many arithmetic progressions along with a set of Banach density zero. In particular, we obtain that given any quasi-projective variety X, any rational map Φ : X −→ X, any subvariety Y ⊆ X, and any point x ∈ ...

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