In mathematical logic, a theory (also called a formal theory) is a set of sentences in a formal language. In most scenarios a deductive system is first...

Mathematical logic is the study of formal logic within mathematics. Major subareas include model theory, proof theory, set theory, and recursion theory...

Andreevich; Maksimova, Larisa (2003). Problems in Set Theory, Mathematical Logic, and the Theory of Algorithms. New York: Springer. p. 52. ISBN 0306477122...

This is a list of mathematical logic topics. For traditional syllogistic logic, see the list of topics in logic. See also the list of computability and...

Set theory is the branch of mathematical logic that studies sets, which can be informally described as collections of objects. Although objects of any...

the study of mathematics using mathematical methods to produce metatheories, or mathematical theories about other mathematical theories. Early investigations...

A mathematical proof is a deductive argument for a mathematical statement, showing that the stated assumptions logically guarantee the conclusion. The...

Ternary relation Transitive relation Trichotomy (mathematics) Well-founded relation Mathematical logic Set theory  (list) Aleph null Bijection, injection and...

with that property. Computability theory is closely related to the branch of mathematical logic called recursion theory, which removes the restriction of...

Proof theory is a major branch of mathematical logic and theoretical computer science within which proofs are treated as formal mathematical objects, facilitating...

Mathematical Logic, John Wiley and Sons, 1967. F. R. Drake, Set theory: An introduction to large cardinals (1974) Rogers, R. L., Mathematical Logic and...

mathematical logic, independence is the unprovability of a sentence from other sentences. A sentence σ is independent of a given first-order theory T...

important theorems. In mathematical logic, the concepts of theorems and proofs have been formalized in order to allow mathematical reasoning about them...

explicitly. In most mathematical endeavours, not much attention is paid to the sorts. A many-sorted logic however naturally leads to a type theory. As Bart Jacobs...

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

In mathematical logic, a theory is complete if it is consistent and for every closed formula in the theory's language, either that formula or its negation...

(1976). Mathematical Logic. Springer. ISBN 9780387901701. Tarski, A.; Mostovski, A.; Robinson, R. (1953), Undecidable Theories, Studies in Logic and the...

identical at first, but fuzzy logic uses degrees of truth as a mathematical model of vagueness, while probability is a mathematical model of ignorance. A basic...

In mathematics and logic, a higher-order logic (abbreviated HOL) is a form of logic that is distinguished from first-order logic by additional quantifiers...

Discrete mathematics is the study of mathematical structures that can be considered "discrete" (in a way analogous to discrete variables, having a bijection...

foundations of mathematics started at the end of the 19th century and formed a new mathematical discipline called mathematical logic, which later had...

Aristotelian logic, although in contemporary mathematical logic the term satisfiable is used instead. The syntactic definition states a theory T {\displaystyle...

Computability theory, also known as recursion theory, is a branch of mathematical logic, computer science, and the theory of computation that originated...

The term mathematical theory may refer to: Theory (mathematical logic), a collection of sentences in a formal language. Mathematical theory, a branch of...

In mathematical logic, a theory is categorical if it has exactly one model (up to isomorphism). Such a theory can be viewed as defining its model, uniquely...

In logic, especially mathematical logic, a signature lists and describes the non-logical symbols of a formal language. In universal algebra, a signature...

validate and discover new mathematical theorems and proofs. There has always been a strong influence from mathematical logic on the field of artificial...

timeline of mathematical logic; see also history of logic. 1847 – George Boole proposes symbolic logic in The Mathematical Analysis of Logic, defining what...

dynamical systems, mathematical dynamical systems theory or the mathematical theory of dynamical systems. Dynamical systems theory and chaos theory deal with the...

In mathematical logic, a sentence (or closed formula) of a predicate logic is a Boolean-valued well-formed formula with no free variables. A sentence...