Computable model theory is a branch of

model theory In mathematical logic, model theory is the study of the relationship between theory (mathematical logic), formal theories (a collection of Sentence (mathematical logic), sentences in a formal language expressing statements about a Structure (mat ...

which deals with questions of

computability Computability is the ability to solve a problem by an effective procedure. It is a key topic of the field of computability theory within mathematical logic and the theory of computation within computer science. The computability of a problem is c ...

as they apply to model-theoretical structures. 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. Computable model theory was developed almost simultaneously by mathematicians in the West, primarily located in the

United States The United States of America (USA), also known as the United States (U.S.) or America, is a country primarily located in North America. It is a federal republic of 50 U.S. state, states and a federal capital district, Washington, D.C. The 48 ...

and

Australia Australia, officially the Commonwealth of Australia, is a country comprising mainland Australia, the mainland of the Australia (continent), Australian continent, the island of Tasmania and list of islands of Australia, numerous smaller isl ...

, and

Soviet The Union of Soviet Socialist Republics. (USSR), commonly known as the Soviet Union, was a List of former transcontinental countries#Since 1700, transcontinental country that spanned much of Eurasia from 1922 until Dissolution of the Soviet ...

Russia Russia, or the Russian Federation, is a country spanning Eastern Europe and North Asia. It is the list of countries and dependencies by area, largest country in the world, and extends across Time in Russia, eleven time zones, sharing Borders ...

during the middle of the 20th century. Because of the

Cold War The Cold War was a period of global Geopolitics, geopolitical rivalry between the United States (US) and the Soviet Union (USSR) and their respective allies, the capitalist Western Bloc and communist Eastern Bloc, which lasted from 1947 unt ...

there was little communication between these two groups and so a number of important results were discovered independently.

References

*. {{mathlogic-stub Constructivism (mathematics) Model theory

See also

References