Menu
Home
People
Places
Arts
History
Plants & Animals
Science
Life & Culture
Technology
Reference.org
Axiom schema of specification
open-in-new
<p>In many popular versions of <a href="/facts/Axiomatic_set_theory/1ptfsvUP">axiomatic set theory</a>, the axiom schema of specification, also known as the axiom schema of separation (<i>Aussonderungsaxiom</i>), subset axiom, axiom of class construction, or axiom schema of restricted comprehension is an <a href="/facts/Axiom_schema/vKNTz5IT">axiom schema</a>. Essentially, it says that any definable <a href="/facts/Subclass_(set_theory)/FjTF1nAr">subclass</a> of a set is a set. </p><p>Some mathematicians call it the axiom schema of comprehension, although others use that term for <i>unrestricted</i> comprehension, discussed below. </p><p>Because restricting comprehension avoided <a href="/facts/Russell%27s_paradox/XupqWGYt">Russell's paradox</a>, several mathematicians including <a href="/facts/Ernst_Zermelo/uvW8gDq0">Zermelo</a>, <a href="/facts/Abraham_Fraenkel/Hc8IBfmY">Fraenkel</a>, and <a href="/facts/G%C3%B6del/P14DqKqK">Gödel</a> considered it the most important axiom of set theory. </p>