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Cosa (chi) è Axiom of Comprehension - definizione

AXIOM SCHEMA

Axiom of specification; Axiom of separation; Axiom schema of separation; Axiom schema of comprehension; Axiom of comprehension; Unrestricted comprehension; Axiom of abstraction; Axiom of subsets; Axioms of subsets; Subset axiom; Axiom schema of restricted comprehension; Comprehension axiom; Aussonderungsaxiom; Axiom schema of unrestricted comprehension; Unrestricted comprehension principle

Axiom of Comprehension

<mathematics> An axiom schema of set theory which states: if P(x) is a property then x : P is a set. I.e. all the things with some property form a set. Acceptance of this axiom leads to Russell's Paradox which is why Zermelo set theory replaces it with a restricted form. (1995-03-31)

Axiom schema of specification

In many popular versions of axiomatic set theory, the axiom schema of specification, also known as the axiom schema of separation, subset axiom scheme or axiom schema of restricted comprehension is an axiom schema. Essentially, it says that any definable subclass of a set is a set.

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

Axiom of extensionality

AXIOM OF ZERMELO–FRAENKEL SET THEORY ASSERTING THAT SET EQUALITY IS DETERMINED BY THE MEMBERSHIP RELATION

Axiom of extension; Axiom of Extensionality; Axiom extensionality; Extensionality axiom; Axiom of equality

In axiomatic set theory and the branches of logic, mathematics, and computer science that use it, the axiom of extensionality, or axiom of extension, is one of the axioms of Zermelo–Fraenkel set theory. It says that sets having the same elements are the same set.

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

Wikipedia

Axiom schema of specification

In many popular versions of axiomatic set theory, the axiom schema of specification, also known as the axiom schema of separation, subset axiom scheme or axiom schema of restricted comprehension is an axiom schema. Essentially, it says that any definable subclass of a set is a set.

Some mathematicians call it the axiom schema of comprehension, although others use that term for unrestricted comprehension, discussed below.

Because restricting comprehension avoided Russell's paradox, several mathematicians including Zermelo, Fraenkel, and Gödel considered it the most important axiom of set theory.

https://en.wikipedia.org/wiki/Axiom schema of specification