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 81 Next

Displaying 1601 – 1620 of 5989

Showing per page

Examples of non-shy sets

Randall Dougherty (1994)

Fundamenta Mathematicae

Christensen has defined a generalization of the property of being of Haar measure zero to subsets of (abelian) Polish groups which need not be locally compact; a recent paper of Hunt, Sauer, and Yorke defines the same property for Borel subsets of linear spaces, and gives a number of examples and applications. The latter authors use the term “shyness” for this property, and “prevalence” for the complementary property. In the present paper, we construct a number of examples of non-shy Borel sets...

Examples of ε-exhaustive pathological submeasures

Ilijas Farah (2004)

Fundamenta Mathematicae

For any given ε > 0 we construct an ε-exhaustive normalized pathological submeasure. To this end we use potentially exhaustive submeasures and barriers of finite subsets of ℕ.

Existence d'un contrôle optimal via l'analyse non standard.

Patricia Spinelli, Georges Solay Rakotonirayni (1991)

Collectanea Mathematica

In this article, we want to show that it is possible to give a complete theory about the existence of an optimal control, without introducing any functional space, by means of the Non Standard Analysis.

Existentially closed II₁ factors

Ilijas Farah, Isaac Goldbring, Bradd Hart, David Sherman (2016)

Fundamenta Mathematicae

We examine the properties of existentially closed ( ω -embeddable) II₁ factors. In particular, we use the fact that every automorphism of an existentially closed ( ω -embeddable) II₁ factor is approximately inner to prove that Th() is not model-complete. We also show that Th() is complete for both finite and infinite forcing and use the latter result to prove that there exist continuum many nonisomorphic existentially closed models of Th().

Expansions of o-minimal structures by sparse sets

Harvey Friedman, Chris Miller (2001)

Fundamenta Mathematicae

Given an o-minimal expansion ℜ of the ordered additive group of real numbers and E ⊆ ℝ, we consider the extent to which basic metric and topological properties of subsets of ℝ definable in the expansion (ℜ,E) are inherited by the subsets of ℝ definable in certain expansions of (ℜ,E). In particular, suppose that f ( E m ) has no interior for each m ∈ ℕ and f : ℝ m → ℝ definable in ℜ, and that every subset of ℝ definable in (ℜ,E) has interior or is nowhere dense. Then every subset of ℝ definable in (ℜ,(S)) has interior...

Expansions of subfields of the real field by a discrete set

Philipp Hieronymi (2011)

Fundamenta Mathematicae

Let K be a subfield of the real field, D ⊆ K be a discrete set and f: Dⁿ → K be such that f(Dⁿ) is somewhere dense. Then (K,f) defines ℤ. We present several applications of this result. We show that K expanded by predicates for different cyclic multiplicative subgroups defines ℤ. Moreover, we prove that every definably complete expansion of a subfield of the real field satisfies an analogue of the Baire category theorem.

Expansions of the real line by open sets: o-minimality and open cores

Chris Miller, Patrick Speissegger (1999)

Fundamenta Mathematicae

The open core of a structure ℜ := (ℝ,<,...) is defined to be the reduct (in the sense of definability) of ℜ generated by all of its definable open sets. If the open core of ℜ is o-minimal, then the topological closure of any definable set has finitely many connected components. We show that if every definable subset of ℝ is finite or uncountable, or if ℜ defines addition and multiplication and every definable open subset of ℝ has finitely many connected components, then the open core of ℜ is...

Currently displaying 1601 – 1620 of 5989