countability

But our need is being opposed by this group, which has no formal ac- countability for the safety of anyone.

Why does Cantor's article emphasize the countability of the algebraic numbers?

Law of Countability: There are at most countably many events.

Other properties, such as countability, are not absolute.

The definition of countability requires that a certain one-to-one correspondence, which is itself a set, must exist.

"Doesn't there have to be some sort of ac- countability, in a matter of such importance?"

For example, second countability and metrisability are hereditary properties.

Size matters: Towards a syntactic decomposition of countability.

From their point of view, Skolem's paradox simply shows that countability is not an absolute property in first order logic.

In terms of countability axioms, it is first-countable and separable, but not second-countable.

In case of infinite countability, this set must obey the (crucial) finiteness condition:

However, not all languages have a grammatical category of number, and those that do do not necessarily view countability in the same terms.

Like other countability axioms, the property of being second-countable restricts the number of open sets that a space can have.

Countability of the model relies on the Löwenheim-Skolem theorem.

Countability (first but not second)

For the question of the countability of objects of interpretation as well as interpretations themselves is ontological.

Notice how, to preserve properties such as local connectedness, second countability, local compactness etc .

Weierstrass probably urged Cantor to publish because he found the countability of the set of algebraic numbers both surprising and useful.

Important countability axioms for topological spaces:

This counterintuitive situation came to be known as Skolem's paradox; it shows that the notion of countability is not absolute.

In her mind there was a simple causal chain lying behind fundamental liberties: increased openness ensured ac- countability, which in turn maintained freedom.

Contrast separability with the related notion of second countability, which is in general stronger but equivalent on the class of metrizable spaces.

Dauben argues that to avoid publication problems, Cantor wrote his article to emphasize the countability of the set of real algebraic numbers.

Why did Cantor emphasize the countability of the real algebraic numbers rather than the uncountability of the real numbers?

They were described on barn swallows, and because of easy countability, many evolutionary, ecological, and behavioral publications use them to quantify the intensity of infestation.