Mathematical logic is the study of formal logic within mathematics. Major subareas include model theory, proof theory, set theory, and recursion theory...
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Igor Andreevich; Maksimova, Larisa (2003). Problems in Set Theory, Mathematical Logic, and the Theory of Algorithms. New York: Springer. p. 52. ISBN 0306477122...
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addresses the mathematical properties of formal systems of logic. However, it can also include attempts to use logic to analyze mathematical reasoning or...
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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...
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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...
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not support it. Quine, W.V. (1981): Mathematical Logic, §6 Hintikka, Jaakko (1998), The Principles of Mathematics Revisited, Cambridge University Press...
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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...
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In mathematical logic, a judgment (or judgement) or assertion is a statement or enunciation in a metalanguage. For example, typical judgments in first-order...
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First-order logic—also called predicate logic, predicate calculus, quantificational logic—is a collection of formal systems used in mathematics, philosophy...
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Consistency (redirect from Consistency (mathematical logic))
what consistent meant in traditional Aristotelian logic, although in contemporary mathematical logic the term satisfiable is used instead. In a sound formal...
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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...
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In mathematical logic, independence is the unprovability of a sentence from other sentences. A sentence σ is independent of a given first-order theory...
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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...
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In mathematical logic, a tautology (from Ancient Greek: ταυτολογία) is a formula or assertion that is true in every possible interpretation. An example...
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20th century or had not previously been considered as mathematics, such as mathematical logic and foundations. Number theory began with the manipulation...
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A mathematical proof is a deductive argument for a mathematical statement, showing that the stated assumptions logically guarantee the conclusion. The...
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validate and discover new mathematical theorems and proofs. There has always been a strong influence from mathematical logic on the field of artificial...
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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...
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from a formula, the former denoting a mathematical object, and the latter denoting a statement about mathematical objects. This is analogous to natural...
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foundational crisis of mathematics. The resolution of this crisis involved the rise of a new mathematical discipline called mathematical logic that includes set...
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proof used in mathematics, a hearkening back to the Greek tradition. The development of the modern "symbolic" or "mathematical" logic during this period...
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Formal language (redirect from Language (mathematical logic))
power. In logic and the foundations of mathematics, formal languages are used to represent the syntax of axiomatic systems, and mathematical formalism...
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Well-formed formula (redirect from Formula (mathematical logic))
In mathematical logic, propositional logic and predicate logic, a well-formed formula, abbreviated WFF or wff, often simply formula, is a finite sequence...
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Soundness (redirect from Unsound (logic))
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...
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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...
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In mathematics, equality is a relationship between two quantities or, more generally, two mathematical expressions, asserting that the quantities have...
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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...
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used in mathematical logic and computer science. Mathematical induction in this extended sense is closely related to recursion. Mathematical induction...
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calculus Predicate (mathematical logic) Predicate logic Predicate variable Quantification Second-order predicate Sentence (mathematical logic) Universal instantiation...
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Axiom (redirect from Mathematical assumption)
Modern mathematics formalizes its foundations to such an extent that mathematical theories can be regarded as mathematical objects, and mathematics itself...
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