All a b c d e f g h i j k l m n o p q r s t u v w x y z Other

Previous Page 39 Next

Displaying 761 – 780 of 1342

Showing per page

Semi-monotone sets

Saugata Basu, Andrei Gabrielov, Nicolai Vorobjov (2013)

Journal of the European Mathematical Society

A coordinate cone in ℝ n is an intersection of some coordinate hyperplanes and open coordinate half-spaces. A semi-monotone set is an open bounded subset of ℝ n , definable in an o-minimal structure over the reals, such that its intersection with any translation of any coordinate cone is connected. This notion can be viewed as a generalization of convexity. Semi-monotone sets have a number of interesting geometric and combinatorial properties. The main result of the paper is that every semi-monotone...

Separable reduction theorems by the method of elementary submodels

Marek Cúth (2012)

Fundamenta Mathematicae

We simplify the presentation of the method of elementary submodels and we show that it can be used to simplify proofs of existing separable reduction theorems and to obtain new ones. Given a nonseparable Banach space X and either a subset A ⊂ X or a function f defined on X, we are able for certain properties to produce a separable subspace of X which determines whether A or f has the property in question. Such results are proved for properties of sets: of being dense, nowhere dense, meager, residual...

Sequent Calculus, Derivability, Provability. Gödel's Completeness Theorem

Marco Caminati (2011)

Formalized Mathematics

Fifth of a series of articles laying down the bases for classical first order model theory. This paper presents multiple themes: first it introduces sequents, rules and sets of rules for a first order language L as L-dependent types. Then defines derivability and provability according to a set of rules, and gives several technical lemmas binding all those concepts. Following that, it introduces a fixed set D of derivation rules, and proceeds to convert them to Mizar functorial cluster registrations...

Small profinite m-stable groups

Frank O. Wagner (2003)

Fundamenta Mathematicae

A small profinite m-stable group has an open abelian subgroup of finite ℳ-rank and finite exponent.

Some combinatorial principles defined in terms of elementary submodels

Sakaé Fuchino, Stefan Geschke (2004)

Fundamenta Mathematicae

We give an equivalent, but simpler formulation of the axiom SEP, which was introduced in [9] in order to capture some of the combinatorial behaviour of models of set theory obtained by adding Cohen reals to a model of CH. Our formulation shows that many of the consequences of the weak Freese-Nation property of 𝒫(ω) studied in [6] already follow from SEP. We show that it is consistent that SEP holds while 𝒫(ω) fails to have the (ℵ₁,ℵ ₀)-ideal property introduced in [2]. This answers a question...

Some decidable congruences of free monoids

Jaroslav Ježek (1999)

Czechoslovak Mathematical Journal

Let W be the free monoid over a finite alphabet A . We prove that a congruence of W generated by a finite number of pairs 〈 a u , u 〉 , where a ∈ A and u ∈ W , is always decidable.

Currently displaying 761 – 780 of 1342