Mathematical logic

Mathematical logic is a subfield of mathematics exploring the applications of formal logic to mathematics. It bears close connections to metamathematics, the foundations of mathematics, and theoretical computer science. The unifying themes in mathematical logic include the study of the expressive power of formal systems and the deductive power of formal proof systems.

Mathematical logic is often divided into the fields of set theory, model theory, recursion theory, and proof theory. These areas share basic results on logic, particularly first-order logic, and definability. In computer science (particularly in the ACM Classification) mathematical logic encompasses additional topics not detailed in this article; see Logic in computer science for those.

Since its inception, mathematical logic has both contributed to, and has been motivated by, the study of foundations of mathematics. This study began in the late 19th century with the development of axiomatic frameworks for geometry, arithmetic, and analysis. In the early 20th century it was shaped by David Hilbert's program to prove the consistency of foundational theories. Results of Kurt Gödel, Gerhard Gentzen, and others provided partial resolution to the program, and clarified the issues involved in proving consistency. Work in set theory showed that almost all ordinary mathematics can be formalized in terms of sets, although there are some theorems that cannot be proven in common axiom systems for set theory. Contemporary work in the foundations of mathematics often focuses on establishing which parts of mathematics can be formalized in particular formal systems (as in reverse mathematics) rather than trying to find theories in which all of mathematics can be developed.

Boolean-valued function

A boolean-valued function (sometimes called a predicate or a proposition) is a function of the type f : X → B, where X is an arbitrary set and where B is a boolean domain, i.e. a generic two-element set, (for example B = {0, 1}), whose elements are interpreted as logical values, for example, 0 = false and 1 = true.

In the formal sciences, mathematics, mathematical logic, statistics, and their applied disciplines, a boolean-valued function may also be referred to as a characteristic function, indicator function, predicate, or proposition. In all of these uses it is understood that the various terms refer to a mathematical object and not the corresponding semiotic sign or syntactic expression.

In formal semantic theories of truth, a truth predicate is a predicate on the sentences of a formal language, interpreted for logic, that formalizes the intuitive concept that is normally expressed by saying that a sentence is true. A truth predicate may have additional domains beyond the formal language domain, if that is what is required to determine a final truth value.

LOGIC (electronic cigarette)

LOGIC is an electronic cigarette developed by Logic Technology Development. The electronic cigarette currently holds a 20% market share in U.S. convenience stores. The nicotine is delivered by polyethylene glycol or propolene glycol solution and other additives such as glycerine and flavorings. Propylene glycol is considered to be safe by the FDA for use in food, health and cosmetic products.

In April 2015, Japan Tobacco International agreed to acquire Logic Technology Development.

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Give (Balkan Beat Box album)

Give is the fourth studio album by the Israeli electronica-world fusion trio Balkan Beat Box.

Critical reception

Give received generally favorable reviews from critics, with the exception of a D- from Consequence of Sound's Alex Young. Young wrote that on the album, "the band is able to put checkmarks in all the Balkan Beat Box boxes but fail to meet the standards they set previously in any of them."

Track listing

Charts

Personnel

References

Give (The Bad Plus album)

Give is the third studio album released by The Bad Plus. It contains covers of Ornette Coleman's "Street Woman", The Pixies' "Velouria", and Black Sabbath's "Iron Man".

Track listing

Depending on the pressing, one or both of the following tracks may appear as bonus tracks. The recording of "Knowing Me, Knowing You" is not the same as the one that appeared on The Bad Plus album.

Personnel

References

Cold (Cold album)

Cold is the debut album by American alternative metal band Cold. The album produced two singles: "Go Away" and "Give."

Track listing

All tracks written by Scooter Ward.

Reception

Allmusic gave the album four out of five stars stating "Cold's songwriting isn't always great and they're too concerned with adolescent angst and horror ("Everyone Dies," "Insane," "Serial Killer," etc.), but the band's sound is fully formed, resulting in a strong debut."

Although the album didn't have excellent sales and lacked heavy promotion, it was ranked the 9th best album of 1998 by Kerrang!

Personnel

Production

Mine (novel)

Mine is a novel written by American author Robert R. McCammon. It won the 1990 Bram Stoker Award for Best Novel.

Plot summary

The novel tells the story of Laura Clayborne, a successful journalist, the wife of a stockbroker and mother-to-be. With her life seemingly falling apart, Laura hopes that her newborn son, David, will make her life everything it ought to be.

Mary Terrell, aka Mary Terror, is a survivor of the radical 1960s and a once a member of the fanatical Storm Front Brigade. Mary lives in a hallucinatory world of memories, guns, and above all, murderous rage. After viewing an ad placed in a popular magazine, she becomes convinced that the former leader of the Brigade, Lord Jack, is commanding her to bring him the child she was carrying when her life was suddenly turned upside down.

Mary steals Laura's baby and the manhunt is on. With no help at all Laura sets out on a cross-country trip to reclaim that which is hers. But soon Laura realizes that in order to get back her son and her life she may have to become as savage as the woman she's hunting.