Computable model theory
Encyclopedia
Computable model theory is a branch of model theory
which deals with questions of computability as they apply to model-theoretical structures. It was developed almost simultaneously by mathematicians in the West, primarily located in the United States
and Australia
, and Soviet Russia
during the middle of the 20th century. Because of the Cold War
there was little communication between these two groups and so a number of important results were discovered independently.
Computable model theory introduces the ideas of computable and decidable models and theories and one of the basic problems is discovering whether or not computable or decidable models fulfilling certain model-theoretic conditions can be shown to exist.
Model theory
In mathematics, model theory is the study of mathematical structures using tools from mathematical logic....
which deals with questions of computability as they apply to model-theoretical structures. It was developed almost simultaneously by mathematicians in the West, primarily located in the United States
United States
The United States of America is a federal constitutional republic comprising fifty states and a federal district...
and Australia
Australia
Australia , officially the Commonwealth of Australia, is a country in the Southern Hemisphere comprising the mainland of the Australian continent, the island of Tasmania, and numerous smaller islands in the Indian and Pacific Oceans. It is the world's sixth-largest country by total area...
, and Soviet Russia
Russia
Russia or , officially known as both Russia and the Russian Federation , is a country in northern Eurasia. It is a federal semi-presidential republic, comprising 83 federal subjects...
during the middle of the 20th century. Because of the Cold War
Cold War
The Cold War was the continuing state from roughly 1946 to 1991 of political conflict, military tension, proxy wars, and economic competition between the Communist World—primarily the Soviet Union and its satellite states and allies—and the powers of the Western world, primarily the United States...
there was little communication between these two groups and so a number of important results were discovered independently.
Computable model theory introduces the ideas of computable and decidable models and theories and one of the basic problems is discovering whether or not computable or decidable models fulfilling certain model-theoretic conditions can be shown to exist.