Prove that there is no order relation "<" that satisfies the five order axioms?
4103
Total ordering on complex numbers
40041
Proof of Non-Ordering of Complex Field
126569
Can we find a well ordering on an infinite set with no largest element?
101163
Does there exist a universal formula of first-order logic that is satisfiable only by structures with infinite domains?
6478
Prove that for any infinite poset there is an infinite subset which is either linearly ordered or antichain.
91281
Proving the so-called "Well Ordering Principle"
74377
Is the natural order relation on an idempotent semiring total/linear?
123458
Prove $( \lnot C \implies \lnot B) \implies (B \implies C)$ without the Deduction Theorem
138632
Proof that if $a > 0$, then $\frac{1}{a} > 0$ using just field and order axioms
98963
Prove that neither $A$ nor $B$ is divisible by $5$
108957
Cardinality of a totally ordered union
16971
Prove that no ordinal is an element of itself
39514
how do I prove that $1 > 0$ in an ordered field?
75007
How can I prove this relation between the elementary set theory and the elementary logic?
3902
Does $k+\aleph_0=\mathfrak{c}$ imply $k=\mathfrak{c}$ without the Axiom of Choice?
43024
Well-ordered sets, properties of an element that is not largest in the set
70196
Is there any well-ordered uncountable set of real numbers under the original ordering?