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...

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...

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

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

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

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

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

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

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

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

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

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

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

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

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...

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

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

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

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...

Peter (2005). Fundamentals of Mathematical Logic. A K Peters. ISBN 978-1-56881-262-5. Jech, Thomas (2003). Set Theory: The Third Millennium Edition,...

In mathematical logic, New Foundations (NF) is a non-well-founded, finitely axiomatizable set theory conceived by Willard Van Orman Quine as a simplification...

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

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

judgment in mathematical logic can be exploited also in foundation of type theory as well. Simply typed lambda calculus Mathematical logic Martin-Löf,...

even formal theories are considered as mathematical objects in proof theory. In Philosophy of mathematics, the concept of "mathematical objects" touches...

theorems are two theorems of mathematical logic that are concerned with the limits of provability in formal axiomatic theories. These results, published...

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