Reverse mathematics is a program in mathematical logic that seeks to determine which axioms are required to prove theorems of mathematics. Its defining...

escape (from C/UNIX), reverse slash, slosh, downwhack, backslant, backwhack, bash, reverse slant, reverse solidus, and reversed virgule. As of November 2022[update]...

of mathematics often focuses on establishing which parts of mathematics can be formalized in particular formal systems (as in reverse mathematics) rather...

In mathematics, an element (or member) of a set is any one of the distinct objects that belong to that set. For example, given a set called A containing...

include structural proof theory, ordinal analysis, provability logic, reverse mathematics, proof mining, automated theorem proving, and proof complexity. Much...

sets. The program of reverse mathematics asks which set-existence axioms are necessary to prove particular theorems of mathematics in subsystems of second-order...

In mathematics, a map or mapping is a function in its general sense. These terms may have originated as from the process of making a geographical map:...

Foundations of mathematics are the logical and mathematical framework that allows the development of mathematics without generating self-contradictory...

of objects defined by other predicates. A predicate is a statement or mathematical assertion that contains variables, sometimes referred to as predicate...

nonstandard models of arithmetic. These principles are often used in reverse mathematics to calibrate the axiomatic strength of theorems. Informally, for...

In mathematics, an expression is a written arrangement of symbols following the context-dependent, syntactic conventions of mathematical notation. Symbols...

In mathematics and other fields, a lemma (pl.: lemmas or lemmata) is a generally minor, proven proposition which is used to prove a larger statement....

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

In mathematics, a set is a collection of different things; the things are elements or members of the set and are typically mathematical objects: numbers...

Reverse Mathematics: Proofs from the Inside Out is a book by John Stillwell on reverse mathematics, the process of examining proofs in mathematics to determine...

sense. The power of these theories for developing mathematics is studied in bounded reverse mathematics as can be found in the works of Stephen A. Cook...

In mathematics, a structure on a set (or on some sets) refers to providing or endowing it (or them) with certain additional features (e.g. an operation...

Nash-Williams (1963). It has since become a prominent example in reverse mathematics as a statement that cannot be proved in ATR0 (a second-order arithmetic...

edu. Retrieved 2020-09-04. "Complement (set) Definition (Illustrated Mathematics Dictionary)". www.mathsisfun.com. Retrieved 2020-09-04. The set in which...

A mathematical object is an abstract concept arising in mathematics. Typically, a mathematical object can be a value that can be assigned to a symbol,...

Such subsystems are essential to reverse mathematics, a research program investigating how much of classical mathematics can be derived in certain weak...

In mathematics, a surjective function (also known as surjection, or onto function /ˈɒn.tuː/) is a function f such that, for every element y of the function's...

In mathematics, and particularly in set theory, category theory, type theory, and the foundations of mathematics, a universe is a collection that contains...

Reverse Polish notation (RPN), also known as reverse Łukasiewicz notation, Polish postfix notation or simply postfix notation, is a mathematical notation...

explanation of the symbols used in this article, refer to the table of mathematical symbols. The union of two sets A and B is the set of elements which are...

In mathematics and logic, the term "uniqueness" refers to the property of being the one and only object satisfying a certain condition. This sort of quantification...

analysis. It was introduced by Paul Bernays in a 1942 article in reverse mathematics that explores which set-theoretic axioms are needed to develop analysis...

Stratification has several usages in mathematics. In mathematical logic, stratification is any consistent assignment of numbers to predicate symbols guaranteeing...

theory and its applications throughout mathematics, a class is a collection of sets (or sometimes other mathematical objects) that can be unambiguously defined...

In mathematics, equality is a relationship between two quantities or expressions, stating that they have the same value, or represent the same mathematical...