Reduced direct products

Frayne, T.; Morel, A. C.; Scott, David

doi:10.4064/fm-51-3-195-228

Cited by 199 publications

(123 citation statements)

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“…The "iP in Theorem 2 is due to Chang [4 ing that 2 a =a + for some infinite cardinal a not less than the number of sentences needed to characterize the given EC A-Since a conjunction of Horn sentences is equivalent to a Horn sentence, it is clear that an EC is an HCA iff it is an HC; hence Theorem 1 is included in Theorem 2.…”

Section: An Ec à Is Closed Under Proper Reduced Products Iff It Is Anmentioning

confidence: 99%

Reduced products, Horn sentences, and decision problems

Galvin¹

1967

Bull. Amer. Math. Soc.

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We shall consider a first order language with equality, and the corresponding structures. Reduced products {powers) and Horn sentences are defined in [4, pp. 199, 211]. An V n sentence is a prenex sentence whose prefix consists of a block of universal quantifiers, followed by a block of existential quantifiers, followed by another block of universal quantifiers, and so on n times; a n sentences are defined dually. An EC (HC, V n C) is the class of all models of an elementary sentence (Horn sentence, V n sentence), and an EC A (HCA, VWCA) is the class of all models of a set of elementary sentences (Horn sentences, V n sentences

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Section: An Ec à Is Closed Under Proper Reduced Products Iff It Is Anmentioning

confidence: 99%

Reduced products, Horn sentences, and decision problems

Galvin¹

1967

Bull. Amer. Math. Soc.

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“…They showed the preservation of the elementary equivalence relation ≡ by arbitrary direct products and also by reduced products over F in. Later Frayne, Morel and Scott ( [17]) noticed that the results extend to arbitrary reduced products (see also [26]). Even though reduced products have been vastly studied for various metric structures, e.g., Banach spaces, C*-algebras, etc., unlike classical first order logic, their model theory has not been studied until very recently in [20] and [15].…”

Section: Introductionmentioning

confidence: 99%

Reduced Products of Metric Structures: A Metric Feferman–vaught Theorem

Ghasemi¹

2016

J. symb. log.

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Abstract. We 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 i M k(i) (C) such that the assertion that their coronas are isomorphic is independent from ZFC, which gives the first example of genuinely non-commutative coronas of separable C*-algebras with this property.

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“…Let G be a lattice-ordered group (/-group) and H a subgroup of G. H is said to be an l-subgroup of G if it is a sublattice of G. H is said to be convex if h u h 2 e H and h± ^ g ^ h 2 imply g e H. The normal convex /-subgroups (/-ideals) of an /-group play the same role in the study of lattice-ordered groups as do normal subgroups in the investigation of groups. For this reason, an /-group is said to be l-simple if it has no non-trivial /-ideals.…”

Section: Introductionmentioning

confidence: 99%

l-simple lattice-ordered groups

Glass

1974

Proceedings of the Edinburgh Mathematical Society

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Let G be a lattice-ordered group (l-group) and H a subgroup of G. H is said to be an l-subgroup of G if it is a sublattice of G. H is said to be convex if h1, h2 ∈ H and h2 ≦ g ≦ h2 imply g ∈ H. The normal convex l-subgroups (l-ideals) of an l-group play the same role in the study of lattice-ordered groups as do normal subgroups in the investigation of groups. For this reason, an l-group is said to be l-simple if it has no non-trivial l-ideals. As in group theory, a central task in the examination of lattice-ordered groups is to characterise those l-groups which are l-simple.

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Reduced direct products

Cited by 199 publications

References 0 publications

Reduced products, Horn sentences, and decision problems

Reduced products, Horn sentences, and decision problems

Reduced Products of Metric Structures: A Metric Feferman–vaught Theorem

l-simple lattice-ordered groups

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