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...

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

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...

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...

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...

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...

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

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

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

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 that is true regardless of the interpretation of its component terms,...

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

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...

argues that mathematical statements are useful fictions that don't correspond to any actual abstract objects. Logicism asserts that all mathematical truths...

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

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

Introduction to Mathematical Logic (3 ed.). New York, Dordrecht, Heidelberg and London: Springer. p. 3. Ladd, Christine (1883). "On the Algebra of Logic". In Peirce...

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...

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...

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

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

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...

identical at first, but fuzzy logic uses degrees of truth as a mathematical model of vagueness, while probability is a mathematical model of ignorance. A basic...

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...

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