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Τι (ποιος) είναι ultraproduct theorem - ορισμός

QUOTIENT OF THE DIRECT PRODUCT OF A FAMILY OF STRUCTURES BY AN ULTRAFILTER

Ultrapower; Los's theorem; Łoś' theorem; Los' theorem; Łoś's Theorem; Łoś's theorem; Los theorem; Ultra power; Ultra product; Los's Theorem; Ultraproducts; The fundamental theorem of ultraproducts; Fundamental theorem of ultraproducts; Ultraproduct monad

Ultraproduct

The ultraproduct is a mathematical construction that appears mainly in abstract algebra and mathematical logic, in particular in model theory and set theory. An ultraproduct is a quotient of the direct product of a family of structures.

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

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.

Βικιπαίδεια

Ultraproduct

The ultraproduct is a mathematical construction that appears mainly in abstract algebra and mathematical logic, in particular in model theory and set theory. An ultraproduct is a quotient of the direct product of a family of structures. All factors need to have the same signature. The ultrapower is the special case of this construction in which all factors are equal.

For example, ultrapowers can be used to construct new fields from given ones. The hyperreal numbers, an ultrapower of the real numbers, are a special case of this.

Some striking applications of ultraproducts include very elegant proofs of the compactness theorem and the completeness theorem, Keisler's ultrapower theorem, which gives an algebraic characterization of the semantic notion of elementary equivalence, and the Robinson–Zakon presentation of the use of superstructures and their monomorphisms to construct nonstandard models of analysis, leading to the growth of the area of nonstandard analysis, which was pioneered (as an application of the compactness theorem) by Abraham Robinson.

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