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)...

In mathematical logic, model theory is the study of the relationship between formal theories (a collection of sentences in a formal language expressing...

the model's structure. In first-order logic, only theories with a finite model can be categorical. Higher-order logic contains categorical theories with...

mathematics, particularly set theory, a finite set is a set that has a finite number of elements. Informally, a finite set is a set which one could in...

A finite-state machine (FSM) or finite-state automaton (FSA, plural: automata), finite automaton, or simply a state machine, is a mathematical model of...

and T that will be satisfied in any model if and only if T is the transitive closure of R. In finite model theory, first-order logic (FO) extended with...

complexity and expressive power of queries, finite model theory, database design theory, dependency theory, foundations of concurrency control and database...

theory, hereditarily finite sets are defined as finite sets whose elements are all hereditarily finite sets. In other words, the set itself is finite...

more specifically in computability theory and computational complexity theory, a model of computation is a model which describes how an output of a mathematical...

In logic, finite model theory, and computability theory, Trakhtenbrot's theorem (due to Boris Trakhtenbrot) states that the problem of validity in first-order...

is an L-theorem if and only if A is a theorem of the theory of finite models of L. If L is finitely axiomatizable (and has a recursive set of inference...

science, Actor model theory concerns theoretical issues for the Actor model. Actors are the primitives that form the basis of the Actor model of concurrent...

born 1934) is a numerical analysis technique used for modeling computational electrodynamics. Finite difference schemes for time-dependent partial differential...

applications of logic to computer science, including database theory, finite model theory, knowledge of multi-agent systems, computer-aided verification...

In the mathematical fields of graph theory and finite model theory, the logic of graphs deals with formal specifications of graph properties using sentences...

Descriptive complexity is a branch of computational complexity theory and of finite model theory that characterizes complexity classes by the type of logic...

as its arguments. Automata theory is closely related to formal language theory. In this context, automata are used as finite representations of formal...

separation; General set theory, a small fragment of Zermelo set theory sufficient for the Peano axioms and finite sets; Kripke–Platek set theory, which omits the...

importance in finite model theory and its applications in computer science (specifically computer aided verification and database theory), since Ehrenfeucht–Fraïssé...

Zbl 0948.68082. Grädel, E. (2007). "Finite Model Theory and Descriptive Complexity". Finite Model Theory and Its Applications (PDF). Springer-Verlag...

complete classification of finite simple groups. Group theory has three main historical sources: number theory, the theory of algebraic equations, and...

products. A model of a Lawvere theory in a category C with finite products is a finite-product preserving functor M : L → C. A morphism of models h : M →...

In universal algebra and in model theory, a structure consists of a set along with a collection of finitary operations and relations that are defined on...

logic. There is a finite second-order theory whose only model is the real numbers if the continuum hypothesis holds and that has no model if the continuum...

such as the theory of algebraically closed fields in a given characteristic. 0 {\displaystyle 0} . Examples: theories with a finite model, and the inconsistent...

Almaden Research Center. He is known for his work in database theory, finite model theory, and reasoning about knowledge. Ron Fagin was born and grew up...

scientist working in the areas of data management, database theory, and finite model theory. The son of two hardware store owners, Abiteboul attended high-school...

infinite model theory. Finite model theory, on the other hand, deals almost exclusively with finite signatures. It is easy to see that for every finite signature...

science and mathematics, the theory of computation is the branch that deals with what problems can be solved on a model of computation, using an algorithm...

In mathematical logic, and particularly in its subfield model theory, a saturated model M is one that realizes as many complete types as may be "reasonably...