There are infinitely many choices of $(\alpha_1,\dots,\alpha_n)$ such that $f(\alpha_1,\dots,\alpha_n)\neq 0$
114146
Polynomial in $n$ variables
144362
The construction of a Vitali set
79187
Can we find $c_n$ to make $X_nc_n \rightarrow 0$ almost surely, even if $EX_n > \infty$?
139078
Infinite partition of $\mathbb N$ by infinite subsets
109054
Given an infinite set of cardinality $X$, is there a chain in $\mathcal P(X)$ of the same cardinalty of $\mathcal P(X)$?
123891
There are finitely many maps on nonnegative integers satisfying $\phi(ab)=\phi(a)+\phi(b)$
5035
Can unprovability unprovable? Is there an $\omega$-fold unprovability?
18634
Combinations of sets raised to the power of a prime modulus: $\binom{p^{\alpha}-1}k \equiv (-1)^k \pmod p$
103732
Proving that for $n \equiv 0 \pmod{2}$, we get ${n \choose 0} < {n \choose 1} <\ldots< {n \choose n/2-1}<{n\choose n/2}$ etc.
150385
The use of the Axiom of Choice in this proof of the sequence lemma
9971
enumerative combinatorics,In how many ways (as a function of n) can one choose a composition α α of n
154578
Proving there is a sequence convergent to a limit point of a set without axiom of countable choice?
96729
Changing the values of an integrable function $f:[a,b] \to \mathbb R$ countably infinitely many points not a dense subset of $[a,b]$
12436
The cardinality of the set of all finite subsets of an infinite set
57644
Lower bounds for ${{2n} \choose {n}}$
19414
Uncountable subset with uncountable complement, without the Axiom of Choice
131592
Finite choice without AC