A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2021; you can also visit the original URL.
The file type is `application/pdf`

.

## Filters

##
###
Projective Limits and Ultraproducts of Nonabelian Finite Groups
[article]

2021
*
arXiv
*
pre-print

This has led to the investigations of the subgroups of metric

arXiv:2107.09900v1
fatcat:jak7m6o6z5abve725hyci35t3a
*ultraproducts*of finite groups. This paper attempts to study the dual problem: what are the quotients of*ultraproducts*of finite groups? ... Since an*ultraproduct*is an abstract quotient of the direct product, this also led to a more general question: what are the abstract quotients of profinite groups? ... The*ultraproduct*functor preserves all finite*limits*. ...##
###
Ultraproducts, p-limits and antichains on the Comfort group order

2004
*
Topology and its Applications
*

*Ultraproducts*have been defined by Lǒs in 1955. ... By hypothesis, there exists, for each ξ ∈ F , z ξ ∈ Φ([c] <ω ) such that z ξ is the p-

*limit*of the sequence {Φ(g ξ (n)): n ∈ ω}. We claim that ξ ∈F z ξ is the p-

*limit*of the sequence {y n : n ∈ ω}. ...

##
###
Ultraproducts and higher order models

1973
*
Bulletin of the Australian Mathematical Society
*

in which these find expression in the

doi:10.1017/s0004972700042568
fatcat:fi4p3rmmrrhynhvjyu6nh2ypcu
*ultraproduct*construction. ... Model theoretic results paralleling those of a first order theory and*ultraproducts*are established. ... Seelye. 315 316 Wi If red Gordon Malcolm an*ultraproduct*of a local family of its substructures are proved. Brief mention is given to the presence of 'inverse*limits*' in this embedding context. ...##
###
Page 649 of Mathematical Reviews Vol. , Issue 82b
[page]

1982
*
Mathematical Reviews
*

It thus provides the theory of nonstandard hulls with immediate contact with constructions in, for example, probability theory that are far from obvious when one’s view is

*limited*solely to the*ultraproduct*... Consider an*ultraproduct*Y of a family [ £;:i€J] of Banach spaces and let Z be the corresponding*ultraproduct*of their dual spaces [E* :i€/]. ...##
###
Ultraproducts and metastability
[article]

2013
*
arXiv
*
pre-print

is the D-

arXiv:1301.3063v4
fatcat:pguw75hjczdwhaapzs33dc4dzi
*limit*of its truth values in the individual structures. ... The constructions above, however, are not*ultraproducts*in the first-order sense, since we restrict to "finite" elements, mod out by infinitesimal proximity ∼, and (implicitly, by taking*limits*with respect ...##
###
Metric ultraproducts of finite simple groups
[article]

2014
*
arXiv
*
pre-print

Then G is isomorphic to an

arXiv:1402.0341v1
fatcat:6uocg7pzcfhvtp3bl5khsi4iby
*ultraproduct*of alternating groups or to an*ultraproduct*of finite simple classical groups. ... The isomorphism type of G determines which of these two cases arises, and, in the latter case, the ω-*limit*of the characteristics of the groups Gi. ... and so the metric*ultraproduct*is a simple group [9] . ...##
###
Remarks on compactifications of pseudofinite groups

2017
*
Fundamenta Mathematicae
*

Basically referring to results in the literature we point out that (i) the Bohr compactification of an

doi:10.4064/fm275-7-2016
fatcat:akkguoqijrgovdt7lfkzlmjl3i
*ultraproduct*of finite simple groups is trivial, and (ii) the "definable" Bohr compactification of ... If bG is the inverse*limit*of a directed system (L i ) i of compact Lie groups, then clearly (bG) 0 is the inverse*limit*of the L 0 i . ... Now def M bG is an inverse*limit*of compact Lie groups L i and we want to show that L 0 i is commutative for each i. ...##
###
Remarks on compactifications of pseudofinite groups
[article]

2015
*
arXiv
*
pre-print

Basically referring to results in the literature we point out (i) the Bohr compactification of an

arXiv:1509.02895v1
fatcat:abtqusnb7bhnnfrygi5s3qqgzq
*ultraproduct*of finite simple groups is trivial, and (ii) the "definable" Bohr compactification of any ... If bG is the inverse*limit*of a directed system (L i ) i of compact Lie groups, then clearly (bG) 0 is the inverse*limit*of the L 0 i . ... Now def M bG is an inverse*limit*of compact Lie groups L i and we want to show that L 0 i is commutative for each i. ...##
###
Some remarks on finitarily approximable groups
[article]

2017
*
arXiv
*
pre-print

Moreover, we discuss the question which connected Lie groups can be embedded into a metric

arXiv:1703.06092v2
fatcat:kflhptymyngcdhevbjl7jeq4cy
*ultraproduct*of finite groups with invariant length function. ... Now it is clear that G, as the inverse*limit*of the groups π J (G) (J ⊆ I finite) and the maps π J (G) → π J ′ (G), contains the inverse*limit*H of the socles of these groups together with the restricted ... Metric*ultraproducts*of groups. ...##
###
Metamathematics of modal logic

1974
*
Bulletin of the Australian Mathematical Society
*

The general concern of this thesis is to explore the relationships between these two semantical frameworks and to discuss their relative strengths and

doi:10.1017/s0004972700041186
fatcat:7f6wejp3y5cn7l3gns75ysz5pe
*limitations*. ... Inverse*limits*of descriptive frames are defined in Section 11, and used in Section 12 in a characterisation, in terms of closure under various constructions, of those classes of descriptive frames that ...##
###
The problem of completeness for Gromov–Hausdorff metrics on C*-algebras

2006
*
Journal of Functional Analysis
*

Conditions ensuring the existence of a C*-structure on the

doi:10.1016/j.jfa.2005.04.007
fatcat:den3li56o5c4lm5nek2zqjradq
*limit*are considered, making use of the notion of*ultraproduct*. ... This is shown by exhibiting a Cauchy sequence whose*limit*, which always exists as an operator system, is not completely order isomorphic to any C*-algebra. ... Furthermore we show that Cauchy sequences are uniformly compact and the Lip-*ultraproduct*is indeed the*limit*. ...##
###
Page 1026 of Mathematical Reviews Vol. 34, Issue 5
[page]

1967
*
Mathematical Reviews
*

The author’s aim is to give an overall view of the work done in

*ultraproducts*and of the part which*ultraproducts*play in the foundations of mathematics. ... of M is not an element of *M,,. | It is, of course, not surprising that some properties of V, | are most easily expressed in terms of the bigger structure | *M_.,; cf. the use of (possibly irrational)*limits*...##
###
Ultraproducts, weak equivalence and sofic entropy
[article]

2015
*
arXiv
*
pre-print

Using this topology, we will show that a profinite action is weakly equivalent to an

arXiv:1509.03189v1
fatcat:sqm53pmuynfsdlyhpjjwrsalla
*ultraproduct*of finite actions. ... We will give a simpler proof of the compactness of the space, showing that convergence is characterized by*ultraproducts*. ... We now show that the*ultraproduct*of a sequence of actions defined in Definition 2.20 is the*limit*with respect to the ultrafilter u for the WC-topology. ...##
###
On the norm of products of polynomials on ultraproduct of Banach spaces
[article]

2014
*
arXiv
*
pre-print

The purpose of this article is to study the problem of finding sharp lower bounds for the norm of the product of polynomials in the

arXiv:1411.5894v1
fatcat:xjgcdpgh3zeafo5zffinjpxg54
*ultraproducts*of Banach spaces (X_i)_ U. ... Later on, we are going to need the next basic Lemma about*limits*of*ultraproducts*, whose proof is an easy exercise of basic topology and ultrafilters. Lemma 2.3. ... Then, the*limit*of (x i ) i∈I respect of U exists and is unique. ...##
###
On the Commutativity of Ultraproducts with Direct Products

1991
*
Proceedings of the American Mathematical Society
*

We show that an

doi:10.2307/2048461
fatcat:zrva2izxw5hp3fm23jzdjixpo4
*ultraproduct*of direct products of structures is elementarily equivalent to a direct product (naturally defined over an*ultraproduct*of sets!) of*ultraproducts*of these structures. ... Let us consider an*ultraproduct*nD(ily(/)), where x'(i) £Fl¡j'i . ... This can be checked directly (the isomorphism being the obviously defined one), or seen as a consequence of a very general algebraic property; namely, that "filtered colimits commute with finite*limits*...
« Previous

*Showing results 1 — 15 out of 2,244 results*