Search results for "Mathematics::Logic"
showing 4 items of 64 documents
More on Finitely Generated Quasivarieties
2015
We begin with the following observation concerning arbitrary finitely generated quasivarieties
The power of procrastination in inductive inference: How it depends on used ordinal notations
1995
We consider inductive inference with procrastination. Usually it is defined using constructive ordinals. For constructive ordinals there exist many different systems of notations. In this paper we study how the power of inductive inference depends on used system of notations.
Noetherian type in topological products
2010
The cardinal invariant "Noetherian type" of a topological space $X$ (Nt(X)) was introduced by Peregudov in 1997 to deal with base properties that were studied by the Russian School as early as 1976. We study its behavior in products and box-products of topological spaces. We prove in Section 2: 1) There are spaces $X$ and $Y$ such that $Nt(X \times Y) < \min\{Nt(X), Nt(Y)\}$. 2) In several classes of compact spaces, the Noetherian type is preserved by the operations of forming a square and of passing to a dense subspace. The Noetherian type of the Cantor Cube of weight $\aleph_\omega$ with the countable box topology, $(2^{\aleph_\omega})_\delta$, is shown in Section 3 to be closely related …
Natural Addition of Ordinals
2019
Summary In [3] the existence of the Cantor normal form of ordinals was proven in the Mizar system [6]. In this article its uniqueness is proven and then used to formalize the natural sum of ordinals.