Reduced products and sheaves of metric structures

2013 ◽  
Vol 59 (3) ◽  
pp. 219-229 ◽  
Author(s):  
Vinicius Cifú Lopes
Keyword(s):  
Reduced Products ◽  
Metric Structures

scholarly journals REDUCED PRODUCTS OF METRIC STRUCTURES: A METRIC FEFERMAN–VAUGHT THEOREM

2016 ◽  
Vol 81 (3) ◽  
pp. 856-875 ◽  
Author(s):  
SAEED GHASEMI
Keyword(s):  
Continuum Hypothesis ◽  
C Algebras ◽  
Reduced Products ◽  
Metric Structures ◽  
The Continuum

AbstractWe extend the classical Feferman–Vaught theorem to logic for metric structures. This implies that the reduced powers of elementarily equivalent structures are elementarily equivalent, and therefore they are isomorphic under the Continuum Hypothesis. We also prove the existence of two separable C*-algebras of the form ⊕iMk(i) (ℂ) such that the assertion that their coronas are isomorphic is independent from ZFC, which gives the first example of genuinely noncommutative coronas of separable C*-algebras with this property.

scholarly journals RIGIDITY OF CONTINUOUS QUOTIENTS

2014 ◽  
Vol 15 (1) ◽  
pp. 1-28 ◽  
Author(s):  
Ilijas Farah ◽  
Saharon Shelah
Keyword(s):  
Connected Space ◽  
Proper Forcing Axiom ◽  
Reduced Products ◽  
Proper Forcing ◽  
Metric Structures ◽  
Continuous Fields ◽  
The Axiom Of Choice ◽  
Metrizable Spaces ◽  
Completely Metrizable ◽  
Index Space

We study countable saturation of metric reduced products and introduce continuous fields of metric structures indexed by locally compact, separable, completely metrizable spaces. Saturation of the reduced product depends both on the underlying index space and the model. By using the Gelfand–Naimark duality we conclude that the assertion that the Stone–Čech remainder of the half-line has only trivial automorphisms is independent from ZFC (Zermelo-Fraenkel axiomatization of set theory with the Axiom of Choice). Consistency of this statement follows from the Proper Forcing Axiom, and this is the first known example of a connected space with this property.

METHODS AND ALGORITHMS FOR THE COMPLETE PROCESSING OF A POSTDETECTOR LOW-CONTRAST OPTICAL IMAGE

2018 ◽  
pp. 99-107
Author(s):  
V. V. Lavrov ◽  
R. S. Luchkin ◽  
O. I. Nemykin ◽  
M. E. Prokhorov ◽  
Yu. G. Ryndin ◽  
...  
Keyword(s):  
Optical Image ◽  
Structural Elements ◽  
Filtration Process ◽  
Low Contrast ◽  
Information Object ◽  
Detection Stage ◽  
Metric Structures ◽  
Spot 5 ◽  
Integrated Indicators ◽  
Complete Processing

Methods and algorithms for the complete processing of a post-detector low-contrast optical image (OI) of an unknown remote object obtained by ground-based optical means of observation under conditions of a complex background situation are considered. The purpose of processing is to separate and interpret at least with the help of the analyst, of the main constructive elements using the integrated indicators introduced in [6] and the characteristics of the analyzed OI, which are connected by the information, topological and metric structures of the OI. The stages of processing the OI include extracting the image-containing information object of the image portion (detection) and filtration of the OI, using recursive rank filtering. The final stages of processing include the segmentation of the OI and the allocation on it constructive elements using the apparatus of graph theory. An example of image processing of a Spot-5 spacecraft obtained in real conditions is given. It is shown that in this case at the detection stage it is possible to reduce the volume of information processed at subsequent stages by 8 times, in the filtration process to increase the compactness of the OI and to increase its connectivity in comparison with the post-detection OI. As a result of segmentation and allocation of constructive elements, three structural elements that can be interpreted as a spacecraft case and two remote panels can be identified with the analyst’s participation.

scholarly journals Proof-theoretic uniform boundedness and bounded collection principles and countable Heine–Borel compactness

2021 ◽  
Author(s):  
Ulrich Kohlenbach
Keyword(s):  
Uniform Boundedness ◽  
Metric Structures

AbstractIn this note we show that proof-theoretic uniform boundedness or bounded collection principles which allow one to formalize certain instances of countable Heine–Borel compactness in proofs using abstract metric structures must be carefully distinguished from an unrestricted use of countable Heine–Borel compactness.

On the mechanism of formation of dimeric and reduced products from an α-halo amide with sodium methoxide

Tetrahedron ◽  
1978 ◽  
Vol 34 (15) ◽  
pp. 2371-2375 ◽  
Author(s):  
Gy. Simig ◽  
K. Lempert ◽  
Zs. Váli ◽  
G. Tóth ◽  
J. Tamás
Keyword(s):  
Sodium Methoxide ◽  
Mechanism Of Formation ◽  
Reduced Products

scholarly journals Omitting types in logic of metric structures

2018 ◽  
Vol 18 (02) ◽  
pp. 1850006 ◽  
Author(s):  
Ilijas Farah ◽  
Menachem Magidor
Keyword(s):  
Complete Theory ◽  
Simple Test ◽  
Finite Sets ◽  
Complete Type ◽  
Metric Structures ◽  
Omitting Types ◽  
Theory Formula

This paper is about omitting types in logic of metric structures introduced by Ben Yaacov, Berenstein, Henson and Usvyatsov. While a complete type is omissible in some model of a countable complete theory if and only if it is not principal, this is not true for the incomplete types by a result of Ben Yaacov. We prove that there is no simple test for determining whether a type is omissible in a model of a theory [Formula: see text] in a countable language. More precisely, we find a theory in a countable language such that the set of types omissible in some of its models is a complete [Formula: see text] set and a complete theory in a countable language such that the set of types omissible in some of its models is a complete [Formula: see text] set. Two more unexpected examples are given: (i) a complete theory [Formula: see text] and a countable set of types such that each of its finite sets is jointly omissible in a model of [Formula: see text], but the whole set is not and (ii) a complete theory and two types that are separately omissible, but not jointly omissible, in its models.

Classification of 3-dimensional left-invariant almost paracontact metric structures

2017 ◽  
Vol 17 (3) ◽  
Author(s):  
Giovanni Calvaruso ◽  
Antonella Perrone
Keyword(s):  
Lie Groups ◽  
Three Dimensional ◽  
Complete Classification ◽  
Natural Assumption ◽  
Geometric Properties ◽  
3 Dimensional ◽  
Metric Structures

AbstractWe study left-invariant almost paracontact metric structures on arbitrary three-dimensional Lorentzian Lie groups. We obtain a complete classification and description under a natural assumption, which includes relevant classes as normal and almost para-cosymplectic structures, and we investigate geometric properties of these structures.

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