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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 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 example of a full wallpaper name in Hermann-Mauguin style (also called IUCr notation) is p31m, with four letters or digits; more usual is a shortened name like cmm or pg. For wallpaper groups the full notation begins with either p or c, for a primitive cell or a face-centred cell; these are explained below.
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 ...
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 mathematical logic, abstract model theory is a generalization of model theory that studies the general properties of extensions of first-order logic and their models. [1] Abstract model theory provides an approach that allows us to step back and study a wide range of logics and their relationships. [2] The starting point for the study of ...
The mental model theory of reasoning was developed by Philip Johnson-Laird and Ruth M.J. Byrne (Johnson-Laird and Byrne, 1991). It has been applied to the main domains of deductive inference including relational inferences such as spatial and temporal deductions; propositional inferences, such as conditional, disjunctive and negation deductions; quantified inferences such as syllogisms; and ...
The social identity model of deindividuation effects (or SIDE model) is a theory developed in social psychology and communication studies. SIDE explains the effects of anonymity and identifiability on group behavior. It has become one of several theories of technology that describe social effects of computer-mediated communication.