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...

of mathematics. The resolution of this crisis involved the rise of a new mathematical discipline called mathematical logic that includes set theory, model...

(1976). Mathematical Logic. Springer. p. 279. ISBN 9780387901701. Tarski, A.; Mostovski, A.; Robinson, R. (1953), Undecidable Theories, Studies in Logic and...

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

In mathematical logic, independence is the unprovability of some specific sentence from some specific set of other sentences. The sentences in this set...

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...

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

of symbolic logic. There are generally two ways that equality is formalized in mathematics: through logic or through set theory. In logic, equality is...

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

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...

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

Categorical logic is the branch of mathematics in which tools and concepts from category theory are applied to the study of mathematical logic. It is also...

foundation of mathematics has been eventually resolved with the rise of mathematical logic as a new area of mathematics. In this framework, a mathematical or logical...

In deductive logic, a consistent theory is one that does not lead to a logical contradiction. A theory T {\displaystyle T} is consistent if there is no...

In mathematical logic the theory of pure equality is a first-order theory. It has a signature consisting of only the equality relation symbol, and includes...

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

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...

the mathematical field of combinatorial game theory, but no mathematics is necessary in order to play it. Mathematical puzzles require mathematics in order...

to reading texts Mathematical theory, an area of mathematical research that is relatively self-contained Theory (mathematical logic), a set of sentences...

model theory, metamathematics, and algebraic logic, he also contributed to abstract algebra, topology, geometry, measure theory, mathematical logic, set...

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

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...

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

formalism of mathematical logic, and is presupposed by contemporary treatments of Peano arithmetic and nearly all treatments of axiomatic set theory. The 1928...

core design of constructive logic using dependent types. Martin-Löf designed the type theory on the principles of mathematical constructivism. Constructivism...

In mathematical logic, algebraic logic is the reasoning obtained by manipulating equations with free variables. What is now usually called classical algebraic...

role in mathematical logic and especially Boolean algebras have major applications in computer science. Finally, various structures in mathematics combine...