Short version: A note of mine was rejected by the arXiv moderation (something I didn't even know was possible) on account of being “unrefereeable”. The moderation process provides absolutely no feedback as to why and does not answer questions. I can think of various reasons but I don't know whi...

Let $\mathcal{A}$ be an arbitrary (typically infinite-dimensional) Banach space with norm $\|\cdot\|_{\mathcal{A}}$ and let $\mathcal{A}^{n}$ be its Cartesian product. I came across the following statement and wonder whether it is true or not: All norms $\|\cdot\|_{\mathcal{A}^{n}}$ on $\mathcal...

Here is a question that popped into my head right as I fell asleep last night. I was thinking about constructions of irrational numbers, like pi. I was wondering if there are two constructions (any constructions, the pair doesn't have to include pi itself) such that: We have good reason to be...

Below, all languages are finite for simplicity. This question is about generalizations of Barwise compactness for logics more complicated than $\mathcal{L}_{\omega_1,\omega}$: properties of the form "For every 'small' $\mathcal{L}$-theory $T$, if every 'relatively simple' $D\subseteq T$ is sat...