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syntactical theorem - Übersetzung nach russisch
математика
синтаксическая теорема
![The divergence theorem can be used to calculate a flux through a [[closed surface]] that fully encloses a volume, like any of the surfaces on the left. It can ''not'' directly be used to calculate the flux through surfaces with boundaries, like those on the right. (Surfaces are blue, boundaries are red.)](https://commons.wikimedia.org/wiki/Special:FilePath/SurfacesWithAndWithoutBoundary.svg?width=200 "The divergence theorem can be used to calculate a flux through a [[closed surface]] that fully encloses a volume, like any of the surfaces on the left. It can ''not'' directly be used to calculate the flux through surfaces with boundaries, like those on the right. (Surfaces are blue, boundaries are red.)")
математика
теорема о дивергенции
теорема Гаусса-Остроградского
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![planar]] map with five colors such that no two regions with the same color meet. It can actually be colored in this way with only four colors. The [[four color theorem]] states that such colorings are possible for any planar map, but every known proof involves a computational search that is too long to check by hand.](https://commons.wikimedia.org/wiki/Special:FilePath/4CT Non-Counterexample 1.svg?width=200 "planar]] map with five colors such that no two regions with the same color meet. It can actually be colored in this way with only four colors. The [[four color theorem]] states that such colorings are possible for any planar map, but every known proof involves a computational search that is too long to check by hand.")
![universality]]) resembles the [[Mandelbrot set]].](https://commons.wikimedia.org/wiki/Special:FilePath/CollatzFractal.png?width=200 "universality]]) resembles the [[Mandelbrot set]].")
![strings of symbols]] may be broadly divided into [[nonsense]] and [[well-formed formula]]s. A formal language can be thought of as identical to the set of its well-formed formulas. The set of well-formed formulas may be broadly divided into theorems and non-theorems.](https://commons.wikimedia.org/wiki/Special:FilePath/Formal languages.svg?width=200 "strings of symbols]] may be broadly divided into [[nonsense]] and [[well-formed formula]]s. A formal language can be thought of as identical to the set of its well-formed formulas. The set of well-formed formulas may be broadly divided into theorems and non-theorems.")
математика
формальная теорема
Definition
Wikipedia
In mathematical logic, Löb's theorem states that in Peano arithmetic (PA) (or any formal system including PA), for any formula P, if it is provable in PA that "if P is provable in PA then P is true", then P is provable in PA. If Prov(P) means that the formula P is provable, we may express this more formally as
- If
- then
An immediate corollary (the contrapositive) of Löb's theorem is that, if P is not provable in PA, then "if P is provable in PA, then P is true" is not provable in PA. For example, "If is provable in PA, then " is not provable in PA.
Löb's theorem is named for Martin Hugo Löb, who formulated it in 1955. It is related to Curry's paradox.
