Computable model theory is a branch of
model theory
In mathematical logic, model theory is the study of the relationship between formal theories (a collection of sentences in a formal language expressing statements about a mathematical structure), and their models (those structures in which the s ...
which deals with questions of
computability
Computability is the ability to solve a problem in an effective manner. 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 close ...
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 (U.S.A. or USA), commonly known as the United States (U.S. or US) or America, is a country primarily located in North America. It consists of 50 states, a federal district, five major unincorporated territorie ...
and
Australia
Australia, officially the Commonwealth of Australia, is a Sovereign state, sovereign country comprising the mainland of the Australia (continent), Australian continent, the island of Tasmania, and numerous List of islands of Australia, sma ...
, and
Soviet
The Soviet Union,. officially the Union of Soviet Socialist Republics. (USSR),. was a List of former transcontinental countries#Since 1700, transcontinental country that spanned much of Eurasia from 1922 to 1991. A flagship communist state, ...
Russia
Russia (, , ), or the Russian Federation, is a List of transcontinental countries, transcontinental country spanning Eastern Europe and North Asia, Northern Asia. It is the List of countries and dependencies by area, largest country in the ...
during the middle of the 20th century. Because of the
Cold War
The Cold War is a term commonly used to refer to a period of geopolitical tension between the United States and the Soviet Union and their respective allies, the Western Bloc and the Eastern Bloc. The term '' cold war'' is used because the ...
there was little communication between these two groups and so a number of important results were discovered independently.
See also
*
Vaught conjecture The Vaught conjecture is a conjecture in the mathematical field of model theory originally proposed by Robert Lawson Vaught in 1961. It states that the number of countable models of a first-order complete theory in a countable language is finite o ...
References
*{{citation, last=Harizanov, first=V. S., authorlink=Valentina Harizanov, contribution=Pure Computable Model Theory, pages=3–114, title=Handbook of Recursive Mathematics, Volume 1: Recursive Model Theory, series=Studies in Logic and the Foundations of Mathematics, volume=138, editor-first=Iurii Leonidovich, editor-last=Ershov, publisher=North Holland, year=1998, isbn=978-0-444-50003-8, mr=1673621.
Constructivism (mathematics)
Model theory