Welcome to the middle attic, where the uncountable cardinals, that solid stock of mathematics, begin their endless upward structural progession. Here, we survey the infinite cardinals whose existence can be proved in, or is at least equiconsistent with, the ZFC axioms of set theory. - into the [](Upper_attic.md) - <a href="Correct" class="mw-redirect" title="Correct">correct</a> cardinals, [](Reflecting.md) and the [](Reflecting.md#Feferman_theory) - [](Reflecting.md#Sigma_2_correct_cardinals) and [$\Sigma_n$-correct](Reflecting.md "Reflecting") cardinals - [0-extendible](Extendible.md#-extendible_cardinals "Extendible") cardinal - [$\Sigma_n$-extendible](Extendible.md#Sigma_n-extendible_cardinals "Extendible") cardinal - [](Beth.md#beth_fixed_point) - the [beth](Beth.md "Beth") numbers and the [](Beth.md) - <a href="Beth_omega" class="mw-redirect" title="Beth omega">$\beth_\omegalt;/a> and the <a href="Strong_limit" class="mw-redirect" title="">strong limit</a> cardinals - <a href="Theta" class="mw-redirect" title="Theta">$\Thetalt;/a> - the [continuum](Continuum.md "Continuum") - [](Cardinal_characteristics.md) of the continuum - the <a href="Bounding_number" class="mw-redirect" title="Bounding number">bounding number $\frak{b}lt;/a>, the <a href="Dominating_number" class="mw-redirect" title="Dominating number">dominating number $\frak{d}lt;/a>, the <a href="Covering_number" class="mw-redirect" title="Covering number">covering numbers</a>, <a href="Additivity_number" class="mw-redirect" title="Additivity number">additivity numbers</a> and many more - the <a href="Descriptive_set_theory" class="mw-redirect" title="Descriptive set theory">descriptive set-theoretic</a> cardinals - [](Aleph.md#aleph_fixed_point) - the [aleph](Aleph.md "Aleph") numbers and the [](Aleph.md) - [](Buchholz's_ψ_functions.md) - [$\aleph_\omega$](Aleph.md#aleph_omega "Aleph") and <a href="Singular" class="mw-redirect" title="Singular">singular</a> cardinals - [$\aleph_2$](Aleph.md#aleph_two "Aleph"), the second uncountable cardinal - <a href="Uncountable" class="mw-redirect" title="Uncountable">uncountable</a>, <a href="Regular" class="mw-redirect" title="Regular">regular</a> and <a href="Successor" class="mw-redirect" title="Successor">successor</a> cardinals - [$\aleph_1$](Aleph.md#aleph_one "Aleph"), the first <a href="Uncountable" class="mw-redirect" title="Uncountable">uncountable</a> cardinal - [cardinals](Cardinal.md "Cardinal"), <a href="Infinite" class="mw-redirect" title="Infinite">infinite</a> cardinals - <a href="Aleph_zero" class="mw-redirect" title="Aleph zero">$\aleph_0lt;/a> and the rest of the [](Lower_attic.md)