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Projective Limits and Ultraproducts of Nonabelian Finite Groups
[article]
2021
arXiv
pre-print
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This has led to the investigations of the subgroups of metric 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. ...
arXiv:2107.09900v1
fatcat:jak7m6o6z5abve725hyci35t3a
Ultraproducts, p-limits and antichains on the Comfort group order
2004
Topology and its Applications
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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}. ...
doi:10.1016/j.topol.2004.02.012
fatcat:d7uykjasl5h7rn5riq4l763flq
Ultraproducts and higher order models
1973
Bulletin of the Australian Mathematical Society
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in which these find expression in the 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. ...
doi:10.1017/s0004972700042568
fatcat:fi4p3rmmrrhynhvjyu6nh2ypcu
Page 649 of Mathematical Reviews Vol. , Issue 82b
[page]
1982
Mathematical Reviews
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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
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is the D-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 ...
arXiv:1301.3063v4
fatcat:pguw75hjczdwhaapzs33dc4dzi
Metric ultraproducts of finite simple groups
[article]
2014
arXiv
pre-print
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Then G is isomorphic to an 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] . ...
arXiv:1402.0341v1
fatcat:6uocg7pzcfhvtp3bl5khsi4iby
Remarks on compactifications of pseudofinite groups
2017
Fundamenta Mathematicae
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Basically referring to results in the literature we point out that (i) the Bohr compactification of an 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. ...
doi:10.4064/fm275-7-2016
fatcat:akkguoqijrgovdt7lfkzlmjl3i
Remarks on compactifications of pseudofinite groups
[article]
2015
arXiv
pre-print
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Basically referring to results in the literature we point out (i) the Bohr compactification of an 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. ...
arXiv:1509.02895v1
fatcat:abtqusnb7bhnnfrygi5s3qqgzq
Some remarks on finitarily approximable groups
[article]
2017
arXiv
pre-print
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Moreover, we discuss the question which connected Lie groups can be embedded into a metric 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. ...
arXiv:1703.06092v2
fatcat:kflhptymyngcdhevbjl7jeq4cy
Metamathematics of modal logic
1974
Bulletin of the Australian Mathematical Society
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The general concern of this thesis is to explore the relationships between these two semantical frameworks and to discuss their relative strengths and 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 ...
doi:10.1017/s0004972700041186
fatcat:7f6wejp3y5cn7l3gns75ysz5pe
The problem of completeness for Gromov–Hausdorff metrics on C*-algebras
2006
Journal of Functional Analysis
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Conditions ensuring the existence of a C*-structure on the 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. ...
doi:10.1016/j.jfa.2005.04.007
fatcat:den3li56o5c4lm5nek2zqjradq
Page 1026 of Mathematical Reviews Vol. 34, Issue 5
[page]
1967
Mathematical Reviews
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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
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Using this topology, we will show that a profinite action is weakly equivalent to an 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. ...
arXiv:1509.03189v1
fatcat:sqm53pmuynfsdlyhpjjwrsalla
On the norm of products of polynomials on ultraproduct of Banach spaces
[article]
2014
arXiv
pre-print
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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 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. ...
arXiv:1411.5894v1
fatcat:xjgcdpgh3zeafo5zffinjpxg54
On the Commutativity of Ultraproducts with Direct Products
1991
Proceedings of the American Mathematical Society
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We show that an 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 ...
doi:10.2307/2048461
fatcat:zrva2izxw5hp3fm23jzdjixpo4
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