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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 ...
Naive set theory - In abstract mathematics, naive set theory1 was the first development of set theory, which was later to be reconstructed as axiomatic set theory. Naive set theory is distinguished from axiomatic set theory by the fact that the former regards sets as collections of objects, called the elements or members of the set, whereas ...
Non-well-founded set theory - Non-well founded set theories are variants of axiomatic set theory which allow sets to contain themselves and otherwise violate the rule of well-foundedness. In non-well founded set theories, the foundation axiom of ZFC is replaced by axioms implying its negation.
Kripke-Platek set theory - The Kripke-Platek axioms of set theory (KP) are a system of axioms of axiomatic set theory. The axiom system is written in first-order logic; it has an infinite number of axioms because an axiom schema is used.
Extending Set Theory - Extends the language of set theory through restricted self-reference and through certain large cardinals. Also discusses higher order set theory and axiomatization through reflection principles.
Set Theory with a Universal Set - List of publications and websites on axiomatic set theories.
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