Axiomatic Set Theory theorem. This system was later refined by Adolf Fraenkel and ThoralfSkolem, giving the axioms used today. Axioms for set theory. http://www.fact-index.com/a/ax/axiomatic_set_theory_1.html
Extractions: Main Page See live article Alphabetical index Set theory is a branch of mathematics and computer science created principally by the German mathematician Georg Cantor at the end of the 19th century . Initially controversial, set theory has come to play the role of a foundational theory in modern mathematics, in the sense of a theory invoked to justify assumptions made in mathematics concerning the existence of mathematical objects (such as numbers or functions) and their properties. Formal versions of set theory also have a foundational role to play as specifying a theoretical ideal of mathematical rigor in proofs. At the same time the basic concepts of set theory are used throughout mathematics, while the subject is pursued in its own right as a speciality by a comparatively small group of mathematicians and logicians . It should be mentioned that there are also mathematicians using and promoting different approaches to the foundations of mathematics. The basic concepts of set theory are set and membership. A set is thought of as any collection of objects, called the
[HM] Mathematical Induction By Carlos Cesar De Araujo It is important to stress the adjective settheoretical above, because ThoralfSkolem (another giant) was the first who saw clearly the huge difference http://mathforum.org/epigone/historia/glilminsnun