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Inspired by this question.
Consider a finite set of integers $A$. Denote by $n A$ the $n$-th sumset, i.e. the set $A + A + ... + A$ ($n$ times). Let $l (X)$ be the number of elements in the largest arithmetic progression in $X$. Is it true that the sequence$$c_n = \frac{l(n A...

In Hartshorne's "Algebraic Geometry", there are some two-star ("**")exercises which were open problems at the time of writing(a lot apparently still are). I wonder what progress has been made onthe problem stated in Exercise I.2.17(d):
It is an unsolved problem whether every closed irreducible curve in$\mathbb{P}^3$ is a set-theoretic intersection of two surfaces....

Is it true that every holomorphic function in the unit disc is the sum of two non-vanishing holomorphic functions ?
The terminology is borrowed from this article.
The answer would be positive if given any sequence of points in the unit disc accumulating to the boundary $a_1,a_2...$ and multiplicites $m_1,m_2 ...$, I can construct a function $f\in \mathcal{O}(\mathbb{D})$ such that for every $i$ there exists $k...

This question is linked to a prior one.
Language: Mono-sorted first order logic with equality and additional primitives of a total unary function $\xi$ signifying is the order of, and the binary relation $ [ \ ] $ signifying predication that is $p[x]$ to be read as $p$ predicates $x$, or equivalently...