Axiom of countability information

In mathematics, an axiom of countability is a property of certain mathematical objects that asserts the existence of a countable set with certain properties...

The axiom of countable choice or axiom of denumerable choice, denoted ACω, is an axiom of set theory that states that every countable collection of non-empty...

(20 axioms) Tarski's axioms (10 axioms and 1 schema) Axiom of Archimedes (real number) Axiom of countability (topology) Dirac–von Neumann axioms Fundamental...

the axiom of choice, abbreviated AC or AoC, is an axiom of set theory equivalent to the statement that a Cartesian product of a collection of non-empty...

assuming the axiom of countable choice, a set is countable if its cardinality (the number of elements of the set) is not greater than that of the natural...

the set (with cardinality ℵ0) of positive integers. If the axiom of countable choice (a weaker version of the axiom of choice) holds, then ℵ0 is smaller...

In mathematics, the axiom of regularity (also known as the axiom of foundation) is an axiom of Zermelo–Fraenkel set theory that states that every non-empty...

Measure of non-compactness Paracompact space Locally compact space Compactly generated space Axiom of countability Sequential space First-countable space...

In mathematics, the axiom of dependent choice, denoted by D C {\displaystyle {\mathsf {DC}}} , is a weak form of the axiom of choice ( A C {\displaystyle...

contradictory. Axiom of constructibility Any set is constructible, often abbreviated as V=L Axiom of countability Every set is hereditarily countable Axiom of countable...

every nonempty open subset of the space contains at least one element of the sequence. Like the other axioms of countability, separability is a "limitation...

of mathematics and philosophy that use it, the axiom of infinity is one of the axioms of Zermelo–Fraenkel set theory. It guarantees the existence of at...

of logic, mathematics, and computer science that use it, the axiom of extensionality, axiom of extension, or axiom of extent, is one of the axioms of...

an axiom schema (plural: axiom schemata or axiom schemas) generalizes the notion of axiom. An axiom schema is a formula in the metalanguage of an axiomatic...

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...

an axiom is a premise or starting point for reasoning. In mathematics, an axiom may be a "logical axiom" or a "non-logical axiom". Logical axioms are...

in ZF (Zermelo–Fraenkel axioms without the axiom of choice) alone. The axiom of countable choice, a weak version of the axiom of choice, is sufficient to...

projective determinacy is the special case of the axiom of determinacy applying only to projective sets. The axiom of projective determinacy, abbreviated PD...

space. An axiom of countability is a property of certain mathematical objects (usually in a category) that requires the existence of a countable set with...

The axiom of constructibility is a possible axiom for set theory in mathematics that asserts that every set is constructible. The axiom is usually written...

mathematical logic, the Peano axioms (/piˈɑːnoʊ/, [peˈaːno]), also known as the Dedekind–Peano axioms or the Peano postulates, are axioms for the natural numbers...

system is any set of primitive notions and axioms to logically derive theorems. A theory is a consistent, relatively-self-contained body of knowledge which...

however, countably compact and thus not Lindelöf (a countably compact space is compact if and only if it is Lindelöf). In terms of axioms of countability, [...

the set of all natural numbers. A set that is equinumerous to a proper subset of itself is called Dedekind-infinite. The axiom of countable choice (ACω)...

In mathematics, the axiom of determinacy (abbreviated as AD) is a possible axiom for set theory introduced by Jan Mycielski and Hugo Steinhaus in 1962...