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. 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.

External links

• Metamath -- the foundations of mathematics explored
• Stanford Encyclopedia of Philosophy entry on Set Theory

For information on the history of the notation see

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• Earliest uses of symbols of set theory and logic
• An overview of set theory including philosophical issues
• Bibliography for alternative set theories allowing a universal set
• Quine's New Foundations Axioms