# Category: Finite model theory

Spectrum of a sentence
In mathematical logic, the spectrum of a sentence is the set of natural numbers occurring as the size of a finite model in which a given sentence is true.
Quantifier rank
In mathematical logic, the quantifier rank of a formula is the depth of nesting of its quantifiers. It plays an essential role in model theory. Notice that the quantifier rank is a property of the for
Parity game
A parity game is played on a colored directed graph, where each node has been colored by a priority – one of (usually) finitely many natural numbers. Two players, 0 and 1, move a (single, shared) toke
Trakhtenbrot's theorem
In logic, finite model theory, and computability theory, Trakhtenbrot's theorem (due to Boris Trakhtenbrot) states that the problem of validity in first-order logic on the class of all finite models i
Logic of graphs
In the mathematical fields of graph theory and finite model theory, the logic of graphs deals with formal specifications of graph properties using sentences of mathematical logic. There are several va
The Strange Logic of Random Graphs
The Strange Logic of Random Graphs is a book on zero-one laws for random graphs. It was written by Joel Spencer and published in 2001 by Springer-Verlag as volume 22 of their book series Algorithms an
Descriptive complexity theory
Descriptive complexity is a branch of computational complexity theory and of finite model theory that characterizes complexity classes by the type of logic needed to express the languages in them. For
Finite model theory
Finite model theory is a subarea of model theory. Model theory is the branch of logic which deals with the relation between a formal language (syntax) and its interpretations (semantics). Finite model
Lindström quantifier
In mathematical logic, a Lindström quantifier is a generalized polyadic quantifier. Lindström quantifiers generalize first-order quantifiers, such as the existential quantifier, the universal quantifi