Search results
Results from the WOW.Com Content Network
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 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 ...
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 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.
The approach applies the mathematical techniques of model theory to the task of syntactic description: a grammar is a theory in the logician's sense (a consistent set of statements) and the well-formed structures are the models that satisfy the theory.
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 ...
Robinson proved that a theory has at most one model companion. Not every theory is model-companionable, e.g. theory of groups. However if T is an -categorical theory, then it always has a model companion. [1] [2] A model completion for a theory T is a model companion T* such that for any model M of T, the theory of T* together with the diagram ...
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 ...