Help me understand the proof that usual ordering $\leq$ is not first-order definable in the structure $\left(\mathbb{N};s\right)$.
133082
In Peano arithmetic, can we define inequality using successor?
67637
How come $\lambda(\mathbb{Q})= \inf\left\{\sum_{n \ge 1} \lambda([a_n,b_n)) : \mathbb{Q} \subset \bigcup_{n \ge 1} [a_n,b_n)\right\} = 0$?
82169
Why does a partially ordered set need to be reflexive?
136274
$n! \leq \left( \frac{n+1}{2} \right)^n$ via induction
73350
Geometric solution to find a Set of totally ordered Subsets of $ \mathbb{N} $ is uncountable
82739
Why is $\alpha \rightarrow \forall x(\alpha)$ not generally correct in first-order logic?
47161
Quick logic question about $P\leftrightarrow Q$, terminology
80996
A canonical construction proving $\left|HK\right| = \left|H\right|\left|K\right| / \left|H \cap K\right|$?
142782
Operator< and strict weak ordering
157806
Order of a element on a Symmetric Group
37061
The order of $ab$ when $a,b$ commute
88442
Prove that there's no ordered basis $E$ in which $T{x\choose y}={0\choose y}$ can be represented as $1\ 2\choose 2\ 4$
65574
How to prove that total number of non-isomorphic labelled trees of order $n$ is $n^{n-2}$?
13807
Is there a way to prove that the order of an element in a Group divides the order of the Group, WITHOUT USING LAGRANGE'S
57724
How to prove boolean ordering question
150385
The use of the Axiom of Choice in this proof of the sequence lemma
91557
Show that total orders are maximal orders