Incompleteness of Robinson's Arithmetic
13436
Robinson arithmetic and its incompleteness
20135
Measure of  reals in $[0,1]$ which don't have $4$ in decimal expansion
154324
preservation of completeness under homeomorphism
32081
The dual version of trichotomy of cardinality without AC
53399
Proof of the uncountability of reals using the diagonal argument—problem?
40048
Finding the fallacy in this broken proof
55199
Number Theory in a Choice-less World
122684
How do you prove Well-Ordering without Mathematical Induction? (and vice-versa)
17290
Solutions for dependency problem in interval arithmetic (remedy for nonexistence of additive inverses)
73230
Roots of the incomplete gamma function
42754
Modular arithmetic: division, fractions, solving linear congruences
21862
Proof of lack of pure prime producing polynomials.
10905
Avoiding negative integers in proof of Fundamental Theorem of Arithmetic
27600
Gödel's (in)completeness theorems and the axiomatization of Euclidean geometry
76892
Factoring inequalities on Double Summation (Donald Knuth's Concrete Mathematics)
34758
Cancellation Law for Direct Sums - What is wrong with this argument?
100720
Negative quotients and their remainders