El Reticulo De Las Logicas De Primer Orden Con Cuantificadores Cardinales.
El sistema dels nombres reals revisat.
Elementare Aussagen zur Arithmetik und Galoistheorie von Funktionenkörpern.
Elementary embeddings in torsion-free hyperbolic groups
We describe first-order logic elementary embeddings in a torsion-free hyperbolic group in terms of Sela’s hyperbolic towers. Thus, if embeds elementarily in a torsion free hyperbolic group , we show that the group can be obtained by successive amalgamations of groups of surfaces with boundary to a free product of 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 and codimension in p-adic fields.
Elementary equivalence of lattices of open sets definable in o-minimal expansions of real closed fields
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...
Elementary interpretations of negationless arithmetic
Elementary proofs and the sums differences problem.
In this paper, we rule out the possibility that a certain method of proof in the sums differences conjecture can settle the Kakeya Conjecture.
Elementary regular rings. II.
Elementary submodels of parametrizable models.
Elementary versions of the Sylvester-Gallai theorem.
Éléments pour l'étude de relations localement définies («infra-relations»). Infra-ordres et relation ternaire d'intermédiarité
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...
Elimination theory for the ring of algebraic integers.
Embedded Lattice and Properties of Gram Matrix
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 algebraic closure spaces in 2-ary closure spaces
Embedding Cohen algebras using pcf theory
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 .
Embedding lattices in the Kleene degrees
Under ZFC+CH, we prove that some lattices whose cardinalities do not exceed can be embedded in some local structures of Kleene degrees.
Embedding of Boolean algebras in Ρ(ω)/fin
Embedding of free Boolean algebras in complete Boolean algebras
Embedding orders into the cardinals with
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 for any regular κ. We use this theorem to show that for all κ, the assumption of 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...