Results 1 to 10 of about 111 (106)

Ultraproducts and Related Constructions

Mathematics, 2022
In this work, we survey some research directions in which the ultraproduct construction and methods based on ultrafilters play significant roles. Rather different areas of mathematics have been considered: topics we are reviewing here include some ...
Gábor Sági
doaj   +1 more source

Minimal lambda-theories by ultraproducts [PDF]

Electronic Proceedings in Theoretical Computer Science, 2013
A longstanding open problem in lambda calculus is whether there exist continuous models of the untyped lambda calculus whose theory is exactly the least lambda-theory lambda-beta or the least sensible lambda-theory H (generated by equating all the ...
Antonio Bucciarelli, Alberto Carraro, Antonino Salibra   +2 more
doaj   +1 more source

Model Theory and Proof Theory of Coalgebraic Predicate Logic [PDF]

Logical Methods in Computer Science, 2018
We propose a generalization of first-order logic originating in a neglected work by C.C. Chang: a natural and generic correspondence language for any types of structures which can be recast as Set-coalgebras.
Tadeusz Litak, Dirk Pattinson, Katsuhiko Sano, Lutz Schröder   +3 more
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Accessible operators on ultraproducts of Banach spaces

Extracta Mathematicae
We address a question by Henry Towsner about the possibility of representing linear operators between ultraproducts of Banach spaces by means of ultraproducts of nonlinear maps.
Félix Cabello Sánchez
doaj   +1 more source

Elementary equivalence and disintegration of tracial von Neumann algebras

Forum of Mathematics, Sigma
We prove an analog of the disintegration theorem for tracial von Neumann algebras in the setting of elementary equivalence rather than isomorphism, showing that elementary equivalence of two direct integrals of tracial factors implies fiberwise ...
David Gao, David Jekel
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Notes on compact nilspaces

Discrete Analysis, 2017
Notes on compact nilspaces, Discrete Analysis 2017:16, 57 pp. This is the second paper in a two-part series. The first paper, [also published in this journal](http://discreteanalysisjournal.com/article/2105-notes-on-nilspaces-algebraic-aspects ...
Pablo Candela
doaj   +1 more source

Ultraproduct invariant logics [PDF]

Proceedings of the American Mathematical Society, 1980
In this paper we give a construction of logics via the property of being preserved from the models to their ultraproduct. Specific examples are given which include some cardinality quantifiers.
openaire   +1 more source

Lifting Results for Finite Dimensions to the Transfinite in Systems of Varieties Using Ultraproducts

Bulletin of the Section of Logic
We redefine a system of varieties definable by a schema of equations to include finite dimensions. Then we present a technique using ultraproducts enabling one to lift results proved for every finite dimension to the transfinite.
Tarek Sayed Ahmed
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On “Ultraproducts in topology”

General Topology and its Applications, 1979
AbstractWe correct an error in the above-mentioned paper and provide a solution to an open problem contained therein.
openaire   +2 more sources

Asymptotic freeness in tracial ultraproducts

Forum of Mathematics, Sigma
We prove novel asymptotic freeness results in tracial ultraproduct von Neumann algebras. In particular, we show that whenever $M = M_1 \ast M_2$ is a tracial free product von Neumann algebra and $u_1 \in \mathscr U(M_1)$ , $u_2 \in ...
Cyril Houdayer, Adrian Ioana
doaj   +1 more source