Set theory
Set theory is the branch of mathematical logic that studies sets, which informally are collections of mathematical objects.
Contents
Description
Although any type of object can be collected into a set, set theory is applied most often to objects that are relevant to mathematics.
The language of set theory can be used in the definitions of nearly all mathematical objects.
History
The modern study of set theory was initiated by Georg Cantor and Richard Dedekind in the 1870s.
Paradoxes in naive set theory
After the discovery of paradoxes in naive set theory, numerous axiom systems were proposed in the early twentieth century, of which the Zermelo–Fraenkel axioms, with the axiom of choice, are the best-known.
Foundational system
Set theory is commonly employed as a foundational system for mathematics, particularly in the form of Zermelo–Fraenkel set theory with the axiom of choice.
Contemporary research
Beyond its foundational role, set theory is a branch of mathematics in its own right, with an active research community.
Contemporary research into set theory includes a diverse collection of topics, ranging from the structure of the real number line to the study of the consistency of large cardinals.
See also
- Combinatorial game theory
- Game theory
- Group theory
- Mathematical logic
- Mathematics
- Large cardinal
- Object-role modeling
- Permutation
- Recursive definition
- Set (mathematics)
- Topology
External links
- Set theory @ Wikipedia
