negation theorem
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Negation — For other uses, see Negation (disambiguation). In logic and mathematics, negation, also called logical complement, is an operation on propositions, truth values, or semantic values more generally. Intuitively, the negation of a proposition is… … Wikipedia
Proof sketch for Gödel's first incompleteness theorem — This article gives a sketch of a proof of Gödel s first incompleteness theorem. This theorem applies to any formal theory that satisfies certain technical hypotheses which are discussed as needed during the sketch. We will assume for the… … Wikipedia
Cox's theorem — Cox s theorem, named after the physicist Richard Threlkeld Cox, is a derivation of the laws of probability theory from a certain set of postulates. This derivation justifies the so called logical interpretation of probability. As the laws of… … Wikipedia
Original proof of Gödel's completeness theorem — The proof of Gödel s completeness theorem given by Kurt Gödel in his doctoral dissertation of 1929 (and a rewritten version of the dissertation, published as an article in 1930) is not easy to read today; it uses concepts and formalism that are… … Wikipedia
Compactness theorem — In mathematical logic, the compactness theorem states that a set of first order sentences has a model if and only if every finite subset of it has a model. This theorem is an important tool in model theory, as it provides a useful method for… … Wikipedia
Tarski's undefinability theorem — Tarski s undefinability theorem, stated and proved by Alfred Tarski in 1936, is an important limitative result in mathematical logic, the foundations of mathematics, and in formal semantics. Informally, the theorem states that arithmetical truth… … Wikipedia
Rice's theorem — In computer science, Rice s theorem named after Henry Gordon Rice (also known as The Rice Myhill Shapiro theorem after Rice and John Myhill) states that, for any non trivial property of partial functions, there exists at least one algorithm for… … Wikipedia
Heine–Cantor theorem — In mathematics, the Heine–Cantor theorem, named after Eduard Heine and Georg Cantor, states that if M is a compact metric space, then every continuous function: f : M rarr; N , where N is a metric space, is uniformly continuous.For instance, if f … Wikipedia
Lindström's theorem — In mathematical logic, Lindström s theorem states that first order logic is the strongest logic (satisfying certain conditions, e.g. closure under classical negation) having both the compactness property and the Downward Löwenheim Skolem property … Wikipedia
Gödel's incompleteness theorems — In mathematical logic, Gödel s incompleteness theorems, proved by Kurt Gödel in 1931, are two theorems stating inherent limitations of all but the most trivial formal systems for arithmetic of mathematical interest. The theorems are of… … Wikipedia
formal logic — the branch of logic concerned exclusively with the principles of deductive reasoning and with the form rather than the content of propositions. [1855 60] * * * Introduction the abstract study of propositions, statements, or assertively used … Universalium
