Results 1 to 10 of about 90 (85)

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.
exaly   +2 more sources

Unitaries in ultraproduct of matrices

Journal of Operator Theory, 2017
We study various conditions under which a unitary in an ultraproduct of matrices is conjugated to an ultraproduct of permutations.
exaly   +3 more sources

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

Asymptotic invariants of lattices in locally compact groups

Comptes Rendus. Mathématique, 2023
The aim of this work is to understand some of the asymptotic properties of sequences of lattices in a fixed locally compact group. In particular we will study the asymptotic growth of the Betti numbers of the lattices renormalized by the covolume and the
Carderi, Alessandro
doaj   +1 more source

Algebraic theory of measure algebras

Доповiдi Нацiональної академiї наук України, 2023
A. Horn and A. Tarski initiated the abstract theory of measure algebras. Independently V. Sushchansky, B. Oliynyk and P. Cameron studied the direct limits of Hamming spaces.
O.O. Bezushchak, B.V. Oliynyk
doaj   +1 more source

Monotone subsequence via ultrapower

Open Mathematics, 2018
An ultraproduct can be a helpful organizing principle in presenting solutions of problems at many levels, as argued by Terence Tao. We apply it here to the solution of a calculus problem: every infinite sequence has a monotone infinite subsequence, and ...
Błaszczyk Piotr, Kanovei Vladimir, Katz Mikhail G., Nowik Tahl   +3 more
doaj   +1 more source

Semicontinuity of structure for small sumsets in compact abelian groups

Discrete Analysis, 2019
Semicontinuity of structure for small sumsets in compact abelian groups, Discrete Analysis 2019:18, 46 pp. The well-known Cauchy-Davenport theorem asserts that if $A$ and $B$ are two subsets of a cyclic group of prime order $p$, then $|A+B|\geq\min\{|A|+
John Griesmer
doaj   +1 more source

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

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

SL$_{4}(\textbf{Z})$ is not purely matricial field

Comptes Rendus. Mathématique
We prove that every non-zero finite dimensional unitary representation of $\mathrm{SL}_{4}(\mathbf{Z})$ contains a non-zero $\mathrm{SL}_{2}(\mathbf{Z})$-invariant vector.
Magee, Michael, de la Salle, Mikael
doaj   +1 more source