Results 251 to 260 of about 4,352 (292)
Some of the next articles are maybe not open access.
On Bourbaki’s axiomatic system for set theory
Synthese, 2014zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Maribel Anacona +2 more
openaire +2 more sources
1978
At the close of the 19th century and the beginning of the 20th, the discovery by Burali-Forti and Russell of the paradoxical nature of the intuitive approach to set theory gave impetus to the axiomatization of the subject. Zermelo’s postulates for set theory were published in 1908.
D. VAN DALEN, H.C. DOETS, H. DE SWART
openaire +2 more sources
At the close of the 19th century and the beginning of the 20th, the discovery by Burali-Forti and Russell of the paradoxical nature of the intuitive approach to set theory gave impetus to the axiomatization of the subject. Zermelo’s postulates for set theory were published in 1908.
D. VAN DALEN, H.C. DOETS, H. DE SWART
openaire +2 more sources
1998
In this chapter, we present the Zermelo-Fraenkel axioms for set theory, and sketch the justification of them from the Zermelo hierarchy of Chapter 2. The axiom whose status is least clear is the Axiom of Choice. As a result, it has received special attention from mathematicians, and consequences of its truth or falsity have been noted in various parts ...
openaire +1 more source
In this chapter, we present the Zermelo-Fraenkel axioms for set theory, and sketch the justification of them from the Zermelo hierarchy of Chapter 2. The axiom whose status is least clear is the Axiom of Choice. As a result, it has received special attention from mathematicians, and consequences of its truth or falsity have been noted in various parts ...
openaire +1 more source
1987
A prime reason for the increase in importance of mathematical logic in this century was the discovery of the paradoxes of set theory and the need for a revision of intuitive (and contradictory) set theory. Many different axiomatic theories have been proposed to serve as a foundation for set theory, but, no matter how they may differ at the fringes ...
openaire +1 more source
A prime reason for the increase in importance of mathematical logic in this century was the discovery of the paradoxes of set theory and the need for a revision of intuitive (and contradictory) set theory. Many different axiomatic theories have been proposed to serve as a foundation for set theory, but, no matter how they may differ at the fringes ...
openaire +1 more source
An axiomatic approach to fuzzy set theory
Information Sciences, 1990The authors attempt to formalize axiomatic fuzzy set theory. The motive underlying their approach is the desire to avoid paradoxes. The set of axioms they exhibit is the minimal set that enables a formal definition of fuzzy sets without assuming a universe of discourse, and requires fewer axioms than any other published formal definition of fuzzy sets.
Dan E. Tamir +3 more
openaire +2 more sources
Set Theory, Axiomatizations of
1981Some statements of the language of set theory are accepted as axioms. They are supposed to reflect “true” properties of sets and are derived from mathematical practice. It should be noted that there are different axiomizations of set theory based on different experiences and intuition.
openaire +1 more source
EXTENSION OF A NEW AXIOMATIC SET THEORY
Russian Academy of Sciences. Izvestiya Mathematics, 1994Summary: A new extended axiomatic system of set theory is presented that consists of three perfectly natural axioms. All the axioms of the Zermelo-Fraenkel system, the generalized axiom of choice, and the generalized continuum hypothesis are proved as theorems in the new extended axiomatic set theory.
openaire +1 more source
ON THE NONEMPTINESS OF CLASSES IN AXIOMATIC SET THEORY
Mathematics of the USSR-Izvestiya, 1978Theorems are proved on the consistency with , for , of each of the following three propositions: (1) there exists an L-minimal (in particular, nonconstructive) such that and , but every of class with constructive code is itself constructive; (2) there exist such that their -degrees differ by a formula from , but not by formulas from with constants from
openaire +2 more sources
The origins of Zermelo's axiomatization of set theory
Journal of Philosophical Logic, 1978What gave rise to Ernst Zermelo's axiomatization of set theory in 1908? According to the usual interpretation, Zermelo was motivated by the set-theoretic paradoxes. This paper argues that Zermelo was primarily motivated, not by the paradoxes, but by the controversy surrounding his 1904 proof that every set can be well-ordered, and especially by a ...
openaire +2 more sources
FOUNDATIONS OF A NEW AXIOMATIC SET THEORY
Mathematics of the USSR-Izvestiya, 1991Summary: A new axiomatic set theory, consisting of four axioms, is presented. In this theory one can prove as theorems all of the axioms of Zermelo- Fraenkel set theory with the axiom of choice (ZFC), except for the axiom of regularity.
openaire +2 more sources