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

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

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

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...

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...

not support it. Quine, W.V. (1981): Mathematical Logic, §6 Hintikka, Jaakko (1998), The Principles of Mathematics Revisited, Cambridge University Press...

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...

In mathematical logic, a judgment (or judgement) or assertion is a statement or enunciation in a metalanguage. For example, typical judgments in first-order...

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

what consistent meant in traditional Aristotelian logic, although in contemporary mathematical logic the term satisfiable is used instead. In a sound formal...

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...

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

Classical logic (or standard logic) or Frege–Russell logic is the intensively studied and most widely used class of deductive logic. Classical logic has had...

In mathematical logic, a tautology (from Ancient Greek: ταυτολογία) is a formula or assertion that is true in every possible interpretation. An example...

20th century or had not previously been considered as mathematics, such as mathematical logic and foundations. Number theory began with the manipulation...

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

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

eventually resolved with the rise of mathematical logic as a new area of mathematics. In this framework, a mathematical or logical theory consists of a formal...

from a formula, the former denoting a mathematical object, and the latter denoting a statement about mathematical objects. This is analogous to natural...

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

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

power. In logic and the foundations of mathematics, formal languages are used to represent the syntax of axiomatic systems, and mathematical formalism...

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

false premises. Soundness has a related meaning in mathematical logic, wherein a formal system of logic is sound if and only if every well-formed formula...

foundation for mathematics comparable to first-order logic plus set theory. It is a form of higher-order logic and closely related to the logics of the HOL...

In mathematics, equality is a relationship between two quantities or, more generally, two mathematical expressions, asserting that the quantities have...

In logic, a quantifier is an operator that specifies how many individuals in the domain of discourse satisfy an open formula. For instance, the universal...

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

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

Modern mathematics formalizes its foundations to such an extent that mathematical theories can be regarded as mathematical objects, and mathematics itself...