Add to ORKGThe axiom of determinateness (AD), first studied by Mycielski and Steinhaus (see [11] and [15]), possesses some desirable consequences which support its position as an alternative to the axiom of choice (AC). For instance, AD implies that all sets of reals are Lebesgue measurable
AbstractWe construct a parametrized framework, at the center of which is a space D and the notion of...
Abstract. This paper presents a formal proof of Vitali’s theorem that not all sets of real numbers c...
This textbook gives an introduction to axiomatic set theory and examines the prominent questions tha...
Working within the Zermelo-Frankel Axioms of set theory, we will introduce two important contradicto...
We define the notion of an ultrafilter on a set, and present three applications. The first is an alt...
It is shown that, within L(R), the smallest inner model of set theory containing the reals, the axio...
Dissertação de Mestrado em Matemática apresentada à Faculdade de Ciências e TecnologiaA análise real...
We let: ZF = the Zermelo-Fraenkel axioms of set theory without the Axiom of Choice„(AC) . ZFC = ZF ...
This is an unpolished exposition of some work in the theory of projective ordinals under the hypoth...
AbstractWe consider axioms asserting that Lebesgue measure on the real line may be extended to measu...
We show that in {bf ZF} set theory without choice, the Ultrafilter mbox{Principle} ({bf UP}) is equi...
It is well-known that if we assume a large class of sets of reals to be determined then we may concl...
In this paper we study the relationship between AD and strong partition properties of cardinals as w...
It is shown that if every real has a sharp and every subset of ω1 is con-structible from a real, the...
The aim of this work is to study the consequences of assuming the axiom of determinacy regarding per...
AbstractWe construct a parametrized framework, at the center of which is a space D and the notion of...
Abstract. This paper presents a formal proof of Vitali’s theorem that not all sets of real numbers c...
This textbook gives an introduction to axiomatic set theory and examines the prominent questions tha...
Working within the Zermelo-Frankel Axioms of set theory, we will introduce two important contradicto...
We define the notion of an ultrafilter on a set, and present three applications. The first is an alt...
It is shown that, within L(R), the smallest inner model of set theory containing the reals, the axio...
Dissertação de Mestrado em Matemática apresentada à Faculdade de Ciências e TecnologiaA análise real...
We let: ZF = the Zermelo-Fraenkel axioms of set theory without the Axiom of Choice„(AC) . ZFC = ZF ...
This is an unpolished exposition of some work in the theory of projective ordinals under the hypoth...
AbstractWe consider axioms asserting that Lebesgue measure on the real line may be extended to measu...
We show that in {bf ZF} set theory without choice, the Ultrafilter mbox{Principle} ({bf UP}) is equi...
It is well-known that if we assume a large class of sets of reals to be determined then we may concl...
In this paper we study the relationship between AD and strong partition properties of cardinals as w...
It is shown that if every real has a sharp and every subset of ω1 is con-structible from a real, the...
The aim of this work is to study the consequences of assuming the axiom of determinacy regarding per...
AbstractWe construct a parametrized framework, at the center of which is a space D and the notion of...
Abstract. This paper presents a formal proof of Vitali’s theorem that not all sets of real numbers c...
This textbook gives an introduction to axiomatic set theory and examines the prominent questions tha...