Model theory | Wikipedia audio article
Channel: wikipedia tts
Date: 2018-12-25

This is an audio version of the Wikipedia Article:
https://en.wikipedia.org/wiki/Model_theory


00:01:22 1 Branches of model theory
00:03:40 2 Universal algebra
00:04:48 3 Finite model theory
00:05:02 4 First-order logic
00:05:15 5 Axiomatizability, elimination of quantifiers, and model-completeness
00:05:29 6 Categoricity
00:05:56 7 Set theory
00:06:09 8 Other basic notions
00:06:30 8.1 Reducts and expansions
00:08:34 8.2 Interpretability
00:09:55 8.3 Using the compactness and completeness theorems
00:15:52 8.4 Types
00:20:23 9 History
00:23:19 10 See also
00:25:02 11 Notes
00:25:12 12 References
00:26:07 12.1 Canonical textbooks
00:26:58 12.2 Other textbooks
00:29:19 12.3 Free online texts
00:34:05 History
00:35:29 See also



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SUMMARY
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In mathematics, model theory is the study of classes of mathematical structures (e.g. groups, fields, graphs, universes of set theory) from the perspective of mathematical logic. The objects of study are models of theories in a formal language. A set of sentences in a formal language is one of the components that form a theory. A model of a theory is a structure (e.g. an interpretation) that satisfies the sentences of that theory.
Model theory recognises and is intimately concerned with a duality: it examines semantical elements (meaning and truth) by means of syntactical elements (formulas and proofs) of a corresponding language.

universal algebra + logic = model theory.
Model theory developed rapidly during the 1990s, and a more modern definition is provided by Wilfrid Hodges (1997):

model theory = algebraic geometry − fields,Other nearby areas of mathematics include combinatorics, number theory, arithmetic dynamics, analytic functions, and non-standard analysis.
In a similar way to proof theory, model theory is situated in an area of interdisciplinarity among mathematics, philosophy, and computer science. The most prominent professional organization in the field of model theory is the Association for Symbolic Logic.