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...
Embedding partially ordered sets into
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 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 relations in the lattice of recursively enumerable sets.
Embedding sums of cancellative modes into semimodules
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.
Embeddings, amalgamation and elementary equivalence: the representation of compact logics
Embeddings into 𝓟(ℕ)/fin and extension of automorphisms
Given a Boolean algebra 𝔹 and an embedding e:𝔹 → 𝓟(ℕ)/fin we consider the possibility of extending each or some automorphism of 𝔹 to the whole 𝓟(ℕ)/fin. Among other things, we show, assuming CH, that for a wide class of Boolean algebras there are embeddings for which no non-trivial automorphism can be extended.
Embeddings into Simple Lattice-ordered Groups with Different First Order Theories.
Embeddings of quasicells of iterative algebras.
Emploi des filtres sur N dans l'étude descriptive des fonctions