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

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

calculus Predicate (mathematical logic) Predicate logic Predicate variable Quantification Second-order predicate Sentence (mathematical logic) Universal instantiation...

is an extension of logic, some or all of mathematics is reducible to logic, or some or all of mathematics may be modelled in logic. Bertrand Russell and...

population. Independence may also refer to: Algebraic independence Independence (graph theory), edge-wise non-connectedness Independence (mathematical logic), logical...

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

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

proof used in mathematics, a hearkening back to the Greek tradition. The development of the modern "symbolic" or "mathematical" logic during this period...

list of mathematical terms; just a selection of typical terms of art that may be encountered. Logic – Study of correct reasoning Modal logic – Type of...

In mathematical logic, propositional logic and predicate logic, a well-formed formula, abbreviated WFF or wff, often simply formula, is a finite sequence...

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...

Basis (linear algebra) Burrows–Abadi–Needham logic Direct proof Generating a vector space Linear independence Polynomial Proof Pumping lemma Simpson's rule...

First-order logic, also called predicate logic, predicate calculus, or quantificational logic, is a collection of formal systems used in mathematics, philosophy...

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

occurrence does not affect the probability of occurrence of another Independence (mathematical logic), unprovability of a sentence (e.g. the Parallel postulate)...

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...

used in mathematical logic and computer science. Mathematical induction in this extended sense is closely related to recursion. Mathematical induction...

In model theory, a branch of mathematical logic, the diagram of a structure is a simple but powerful concept for proving useful properties of a theory...

published by Kurt Gödel in 1931, are important both in mathematical logic and in the philosophy of mathematics. The theorems are widely, but not universally,...

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 tautology (from Ancient Greek: ταυτολογία) is a formula that is true regardless of the interpretation of its component terms,...

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

Formal system – Mathematical model for deduction or proof systems Gödel's incompleteness theorems – Limitative results in mathematical logic Hilbert-style...

relational databases, in the form of relational models. In the context of mathematical logic, the term "model" was first applied in 1940 by the philosopher Willard...

addresses the mathematical properties of formal systems of logic. However, it can also include attempts to use logic to analyze mathematical reasoning or...

mathematics. The resolution of this crisis involved the rise of a new mathematical discipline called mathematical logic, which studies formal logic within...

definite mathematical problem. He proposed a theory of "definiteness" using a semi-intuitionistic subsystem of ZF that accepts classical logic for bounded...

systems of formal logic can be defined via model theory. Specifically, a logic α {\displaystyle \alpha } is said to be as strong as a logic β {\displaystyle...

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