Mathematical Logic and Model Theory

In mathematical logic, the Löwenheim-Skolem theorem is a theorem on the existence and cardinality of models, named after Leopold Löwenheim and Thoralf Skolem.

Vaught proved that the number of countable models of a complete theory cannot be 2.

In mathematical logic, specifically in the discipline of model theory, the Fraïssé limit (also called the Fraïssé construction or Fraïssé amalgamation) is a method used to construct (infinite) mathematical structures from their (finite) substructures.

In the mathematical discipline of model theory, the Ehrenfeucht-Fraïssé game (also called back-and-forth games) is a technique based on game semantics for determining whether two structures are elementarily equivalent.

Despite this, the literature still widely refers to the Ryll-Nardzewski theorem as a name for these conditions.

In modal logic, Sahlqvist formulas are a certain kind of modal formula with remarkable properties.

In mathematics, Wilkie's theorem is a result by Alex Wilkie about the theory of ordered fields with an exponential function, or equivalently about the geometric nature of exponential varieties.

Gödel's incompleteness theorems are two theorems of mathematical logic that are concerned with the limits of provability

In mathematical logic, the compactness theorem states that a set of

Gödel's completeness theorem is a fundamental theorem in mathematical logic that establishes a correspondence between semantic

Tarski in 1933, is an important limitative result in mathematical logic, the foundations of mathematics, and in formal

In mathematical logic, the Paris-Harrington theorem states that a certain

Herbrand's theorem is a fundamental result of mathematical logic obtained by Jacques Herbrand (1930). It essentially

In mathematical logic, Craig's interpolation theorem is a result about

In mathematical logic, the Beth definability theorem is a fundamental

In mathematical logic, Lindström's theorem (named after Swedish logician

joint consistency theorem is an important theorem of mathematical logic. It is related to Craig interpolation and Beth

or substructure preservation theorem, is a result in model theory that states the first-order properties are preserved

In logic, finite model theory, and computability theory, Trakhtenbrot's theorem

In model theory and related areas of mathematics, a type is an

In mathematical logic and computer science, Gabbay's separation theorem

In propositional logic and Boolean algebra, De Morgan's laws, also known

In mathematical logic, the diagonal lemma (also known as diagonalization

In mathematical logic, the Barwise compactness theorem, named after

In mathematical logic and computer science, Kamp's theorem states that

In mathematical logic, Diaconescu's theorem, or the Goodman-Myhill

In mathematical logic, Goodstein's theorem is a statement about the

who presented the theorem in 1959, is a result in mathematical logic that states that no countable nonstandard model