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Etymologie

Was (wer) ist syntactical theorem - definition

THEOREM

Lob's Theorem; Löb's Theorem; Lob's theorem; Loeb's theorem; Loeb theorem; Lob theorem; Löb theorem; Loeb's Theorem

Divergence theorem

$</math> approaches <math>\operatorname{div} \mathbf{F}</math>$

GENERALIZATION OF THE FUNDAMENTAL THEOREM IN VECTOR CALCULUS

Gauss' theorem; Gauss's theorem; Gauss theorem; Ostrogradsky-Gauss theorem; Ostrogradsky's theorem; Gauss's Theorem; Divergence Theorem; Gauss' divergence theorem; Ostrogradsky theorem; Gauss-Ostrogradsky theorem; Gauss Ostrogradsky theorem; Gauss–Ostrogradsky theorem

In vector calculus, the divergence theorem, also known as Gauss's theorem or Ostrogradsky's theorem, reprinted in is a theorem which relates the flux of a vector field through a closed surface to the divergence of the field in the volume enclosed.

https://en.wikipedia.org/wiki/Divergence_theorem

theorem

IN MATHEMATICS, A STATEMENT THAT HAS BEEN PROVED

Theorems; Proposition (mathematics); Theorum; Mathematical theorem; Logical theorem; Formal theorem; Theorem (logic); Mathematical proposition; Hypothesis of a theorem

n.

Proposition (to be demonstrated), position, dictum, thesis.

Well-ordering theorem

SET-THEORETIC THEOREM OR PRINCIPLE, EQUIVALENT TO THE AXIOM OF CHOICE

Well ordering theorem; Zermelo's well-ordering theorem; Wellordering theorem; Zermelo's theorem; Zermelo Theorem

In mathematics, the well-ordering theorem, also known as Zermelo's theorem, states that every set can be well-ordered. A set X is well-ordered by a strict total order if every non-empty subset of X has a least element under the ordering.

https://en.wikipedia.org/wiki/Well-ordering_theorem

Wikipedia

Löb's theorem

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

PA\,\vdash \,{{\rm {Prov}}(P)\rightarrow P}

then

PA\,\vdash \,P

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 $1+1=3$ is provable in PA, then $1+1=3$ " 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.

https://en.wikipedia.org/wiki/Löb's theorem