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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 statements of the theory hold). [1]
In model theory, a branch of mathematical logic, the diagram of a structure is a simple but powerful concept for proving useful properties of a theory, for example the amalgamation property and the joint embedding property, among others.
An interpretation of a structure M in a structure N with parameters (or without parameters, respectively) is a pair (,) where n is a natural number and is a surjective map from a subset of N n onto M such that the -preimage (more precisely the -preimage) of every set X ⊆ M k definable in M by a first-order formula without parameters is definable (in N) by a first-order formula with ...
In the mathematical field of model theory, a theory is called stable if it satisfies certain combinatorial restrictions on its complexity. Stable theories are rooted in the proof of Morley's categoricity theorem and were extensively studied as part of Saharon Shelah's classification theory, which showed a dichotomy that either the models of a theory admit a nice classification or the models ...
In model theory and related areas of mathematics, a type is an object that describes how a (real or possible) element or finite collection of elements in a mathematical structure might behave. More precisely, it is a set of first-order formulas in a language L with free variables x 1 , x 2 ,..., x n that are true of a set of n -tuples of an L ...
In model theory, the case of being algebraically closed and its prime field is especially important. While vector spaces are modular and affine spaces are "almost" modular (i.e. everywhere locally modular), algebraically closed fields are examples of the other extremity, not being even locally modular (i.e. none of the localizations is modular).
Download QR code; Print/export Download as PDF; Printable version; In other projects ... Pages in category "Model theorists" The following 42 pages are in this ...
O-minimal structures originated in model theory and so have a simpler — but equivalent — definition using the language of model theory. [2] Specifically if L is a language including a binary relation <, and (M,<,...) is an L-structure where < is interpreted to satisfy the axioms of a dense linear order, [3] then (M,<,...) is called an o-minimal structure if for any definable set X ⊆ M ...