In
mathematical logic
Mathematical logic is the study of formal logic within mathematics. Major subareas include model theory, proof theory, set theory, and recursion theory. Research in mathematical logic commonly addresses the mathematical properties of formal ...
, abstract model theory is a generalization 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 ...
that studies the general properties of extensions of
first-order logic
First-order logic—also known as predicate logic, quantificational logic, and first-order predicate calculus—is a collection of formal systems used in mathematics, philosophy, linguistics, and computer science. First-order logic uses quanti ...
and their models.
Abstract model theory provides an approach that allows us to step back and study a wide range of logics and their relationships. The starting point for the study of abstract models, which resulted in good examples was
Lindström's theorem In mathematical logic, Lindström's theorem (named after Swedish logician Per Lindström, who published it in 1969) states that first-order logic is the '' strongest logic'' (satisfying certain conditions, e.g. closure under classical negation) h ...
.
In 1974
Jon Barwise
Kenneth Jon Barwise (; June 29, 1942 – March 5, 2000) was an American mathematician, philosopher and logician who proposed some fundamental revisions to the way that logic is understood and used.
Education and career
Born in Independence, ...
provided an
axiomatization
In mathematics and logic, an axiomatic system is any set of axioms from which some or all axioms can be used in conjunction to logically derive theorems. A theory is a consistent, relatively-self-contained body of knowledge which usually contai ...
of abstract model theory.
[J. Barwise, 1974 , Annals of Mathematical Logic 7:221–265]
See also
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Lindström's theorem In mathematical logic, Lindström's theorem (named after Swedish logician Per Lindström, who published it in 1969) states that first-order logic is the '' strongest logic'' (satisfying certain conditions, e.g. closure under classical negation) h ...
*
Institution (computer science) The notion of institution was created by Joseph Goguen and Rod Burstall in the late 1970s, in order to deal with the "population explosion among the logical systems used in computer science". The notion attempts to "formalize the informal" conc ...
*
Institutional model theory
References
Further reading
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Mathematical logic
Metatheorems
Model theory
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