Show that there are exactly $\aleph_1$ nonisomorphic countable well orderings.
127233
Cardinality of order types in $\mathbb{N}$
150605
Existence of a regular uncountable $\aleph_{\alpha}$ without $\mathsf{AC}$
68430
Proving the countability of algebraic numbers
82989
T4 and first countable topology that is non metrizable
86926
Why isn't this a well ordering of $\{A\subseteq\mathbb N\mid A\text{ is infinite}\}$?
153652
Countable ordinals are embeddable in the rationals $\Bbb Q$ -- proofs and their use of AC
4383
Finitely generated monoids - how to show that there is not first order set axiomatizing them.
96025
Showing there is only one isomorphism between well ordered sets using transfinite induction
9074
Example of non-isomorphic structures which are elementarily equivalent
3902
Does $k+\aleph_0=\mathfrak{c}$ imply $k=\mathfrak{c}$ without the Axiom of Choice?
138279
Multiplicative order and powers
91281
Proving the so-called "Well Ordering Principle"
150719
All nonisomorphic trees of order $n$
16534
Can $(\Bbb N,\leq)$ have an $\aleph_0$-categorical theory (in a larger language)?
154474
Image of countable and uncountable sets
129813
Is there an easy proof for ${\aleph_\omega} ^ {\aleph_1} = {2}^{\aleph_1}\cdot{\aleph_\omega}^{\aleph_0}$?
96892
Number of Non-isomorphic models of Set Theory