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

Subdirect productMathematics::LogicPure mathematicsMathematics::General MathematicsMathematics::Rings and AlgebrasMathematics::General TopologyFinitely-generated abelian groupMathematics
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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.

Theoretical computer sciencebusiness.industrymedia_common.quotation_subjectProcrastinationInductive reasoningMachine learningcomputer.software_genreNotationConstructivePower (physics)Mathematics::LogicArtificial intelligencebusinesscomputermedia_commonMathematics
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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 …

Topological manifoldFundamental groupTopological algebraGeneral MathematicsTopological tensor productGeneral Topology (math.GN)Noetherian typeMathematics::General TopologyMathematics - LogicTopological spaceChang’s conjectureTopologyTopological vector spaceTukey mapH-spaceMathematics::LogicFOS: MathematicsPCF theoryTopological ring03E04 54A25 (Primary) 03E55 54B10 54D70 54G10 (Secondary)Box productLogic (math.LO)Mathematics - General TopologyMathematics
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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.

natural sumApplied Mathematicshessenberg sumcantor normal form68t99ordinal numbersAlgebraMathematics::LogicComputational Mathematics03e1003b35QA1-939Natural (music)MathematicsMathematicsFormalized Mathematics
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