Axiomatic set theory - The origins of rigorous set theory - Article Index

Encyclopedia - Axiomatic Set Theory: Encyclopedia - Axiomatic Set Theory
Set theory is a branch of mathematics created principally by the German mathematician Georg Cantor at the end of the 19th century. Initia...   » Read the article

Encyclopedia - Axiomatic Set Theory: Encyclopedia Ii - Axiomatic Set Theory - The Origins Of Rigorous Set Theory
The important idea of Cantor's, which got set theory going as a new field of study, was to define two sets A and B to have the same numbe...   » Read the article

Encyclopedia - Axiomatic Set Theory: Encyclopedia Ii - Axiomatic Set Theory - Objections To Set Theory
Since its inception, there have been some mathematicians who have objected to using set theory as a foundation for mathematics, claiming ...   » Read the article

Encyclopedia - Axiomatic Set Theory: Encyclopedia Ii - Axiomatic Set Theory - Well-foundedness And Hypersets
In 1917, Dmitry Mirimanov (also spelled Mirimanoff) introduced the concept of well-foundedness: a set, x0, is well founded iff it has no...   » Read the article

Encyclopedia - Axiomatic Set Theory: Encyclopedia Ii - Axiomatic Set Theory - Set Theory Zfc Foundations For Mathematics
From these initial axioms for sets one can construct all other mathematical concepts and objects: number - discrete and continuous, order...   » Read the article

Encyclopedia - Axiomatic Set Theory: Encyclopedia Ii - Axiomatic Set Theory - Axioms For Set Theory
The axioms for set theory now most often studied and used, although put in their final form by Skolem, are called the Zermelo-Fraenkel se...   » Read the article

Encyclopedia - Axiomatic Set Theory: Encyclopedia Ii - Axiomatic Set Theory - Independence In Zfc
Many important statements are independent of ZFC, see the list of statements undecidable in ZFC. The independence is usually proved by fo...   » Read the article