Axiomatic set theory | Wikipedia audio article
Channel: wikipedia tts
Date: 25/12/2018

This is an audio version of the Wikipedia Article:
https://en.wikipedia.org/wiki/Set_theory


00:01:08 1 History
00:04:22 2 Basic concepts and notation
00:07:44 3 Some ontology
00:09:02 4 Axiomatic set theory
00:11:47 5 Applications
00:13:37 6 Areas of study
00:13:53 6.1 Combinatorial set theory
00:14:16 6.2 Descriptive set theory
00:15:33 6.3 Fuzzy set theory
00:16:10 6.4 Inner model theory
00:17:33 6.5 Large cardinals
00:18:03 6.6 Determinacy
00:18:54 6.7 Forcing
00:19:42 6.8 Cardinal invariants
00:20:20 6.9 Set-theoretic topology
00:20:58 7 Objections to set theory as a foundation for mathematics
00:23:55 8 See also
00:24:14 9 Notes
00:24:23 10 Further reading
00:26:03 11 External links



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SUMMARY
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Set theory is a branch of mathematical logic that studies sets, which informally are collections of objects. 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 to define nearly all mathematical objects.
The modern study of set theory was initiated by Georg Cantor and Richard Dedekind in the 1870s. After the discovery of paradoxes in naive set theory, such as Russell's paradox, numerous axiom systems were proposed in the early twentieth century, of which the Zermelo–Fraenkel axioms, with or without the axiom of choice, are the best-known.
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. 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.