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Elementary embeddings in torsion-free hyperbolic groups

Chloé Perin (2011)

Annales scientifiques de l'École Normale Supérieure

We describe first-order logic elementary embeddings in a torsion-free hyperbolic group in terms of Sela’s hyperbolic towers. Thus, if H embeds elementarily in a torsion free hyperbolic group Γ , we show that the group Γ can be obtained by successive amalgamations of groups of surfaces with boundary to a free product of  H with some free group and groups of closed surfaces. This gives as a corollary that an elementary subgroup of a finitely generated free group is a free factor. We also consider the...

Elementary equivalence of lattices of open sets definable in o-minimal expansions of real closed fields

Vincent Astier (2013)

Fundamenta Mathematicae

We prove that the boolean algebras of sets definable in elementarily equivalent o-minimal expansions of real closed fields are back-and-forth equivalent, and in particular elementarily equivalent, in the language of boolean algebras with new predicates indicating the dimension, Euler characteristic and open sets. We also show that the boolean algebra of semilinear subsets of [0,1]ⁿ definable in an o-minimal expansion of a real closed field is back-and-forth equivalent to the boolean algebra of definable...

Éléments pour l'étude de relations localement définies («infra-relations»). Infra-ordres et relation ternaire d'intermédiarité

H. Durup (1970)

Mathématiques et Sciences Humaines

Dans les sciences de la nature, et en particulier dans les sciences du comportement, on rencontre fréquemment des relations caractérisées par des propriétés locales. Une famille très vaste de telles relations rassemble celles qui sont définies uniquement par des propriétés portant sur les ensembles d'éléments liés à un même élément, soit par la relation («points vus d'un même point»), soit par son inverse («points d'où l'on voit un même point»). A tout type de relation correspondent ainsi plusieurs...

Embedded Lattice and Properties of Gram Matrix

Yuichi Futa, Yasunari Shidama (2017)

Formalized Mathematics

In this article, we formalize in Mizar [14] the definition of embedding of lattice and its properties. We formally define an inner product on an embedded module. We also formalize properties of Gram matrix. We formally prove that an inverse of Gram matrix for a rational lattice exists. Lattice of Z-module is necessary for lattice problems, LLL (Lenstra, Lenstra and Lov´asz) base reduction algorithm [16] and cryptographic systems with lattice [17].

Embedding Cohen algebras using pcf theory

Saharon Shelah (2000)

Fundamenta Mathematicae

Using a theorem from pcf theory, we show that for any singular cardinal ν, the product of the Cohen forcing notions on κ, κ < ν, adds a generic for the Cohen forcing notion on ν + .

Embedding lattices in the Kleene degrees

Hisato Muraki (1999)

Fundamenta Mathematicae

Under ZFC+CH, we prove that some lattices whose cardinalities do not exceed ℵ 1 can be embedded in some local structures of Kleene degrees.

Embedding orders into the cardinals with D C κ

Asaf Karagila (2014)

Fundamenta Mathematicae

Jech proved that every partially ordered set can be embedded into the cardinals of some model of ZF. We extend this result to show that every partially ordered set can be embedded into the cardinals of some model of Z F + D C < κ for any regular κ. We use this theorem to show that for all κ, the assumption of D C κ does not entail that there are no decreasing chains of cardinals. We also show how to extend the result to and embed into the cardinals a proper class which is definable over the ground model. We use...

Embedding partially ordered sets into ω ω

Ilijas Farah (1996)

Fundamenta Mathematicae

We investigate some natural questions about the class of posets which can be embedded into ⟨ω,≤*⟩. Our main tool is a simple ccc forcing notion H E which generically embeds a given poset E into ⟨ω,≤*⟩ and does this in a “minimal” way (see Theorems 9.1, 10.1, 6.1 and 9.2).

Embedding sums of cancellative modes into semimodules

Anna B. Romanowska, Anna Zamojska-Dzienio (2005)

Czechoslovak Mathematical Journal

A mode (idempotent and entropic algebra) is a Lallement sum of its cancellative submodes over a normal band if it has a congruence with a normal band quotient and cancellative congruence classes. We show that such a sum embeds as a subreduct into a semimodule over a certain ring, and discuss some consequences of this fact. The result generalizes a similar earlier result of the authors proved in the case when the normal band is a semilattice.

Currently displaying 61 – 80 of 217