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It is a little difficult to answer this question without knowing more of your personal circumstances, but aiming to pursue a Masters degree instead of trying to enrol directly in a PhD programme might …

$\def\ha{\mathsf{HA}}\def\down{{\downarrow}}\def\mr{\mathrel{\mathbf q}}$I believe this can be proved in a fairly weak fragment of arithmetic, such as $\mathsf{I\Delta_0+EXP}$, possibly even in a poly …

I'm posting my comments here as an answer. Yes such a group should exist. For example it can be constructed as an inner form of the split adjoint group $G$ of type $E_7$ using the short exact sequence …

The answer to the first question is yes: Global Choice is bi-interpretable with Global Well-Ordering. First, I will prove that a class linear order $(C, <)$ is a well-ordering iff every subset (rather …

This is a well-studied problem with multiple types of answers. $n=50$ is quite small for observing the asymptotic limit shape. Uniform sampling of integer partitions is quite easy and scalable, and w …

I have asked Professor Burq why the inequality holds. He told me that we can add the potential and have an equivalent norm. So it should be $\lesssim$ rigorously.

Given two locally compact spaces $X$ and $Y$ then the product $X \times Y$ is an open subset inside $\overline{X} \times \overline{Y}$, where $\overline{X}$ and $\overline{X}$ are the one point compac …

There does not exist any r.e. theory $T\supseteq\mathsf{ZFC}$ and any set $A$ of arithmetical sentences (true or otherwise) such that $T+A$ is complete and consistent, because ZFC has a truth predicat …

Q: Are there any physical processes from the real world that are modeled by truly random operators that have their components iid / or not iid (in some basis)? A widely studied example of a random mat …

By Iosif Pinelis's answer, there is no function we can really call the $\liminf$. I think Will Sawin / Aleksei Kulikov showed $\limsup_{n \to \infty} \frac{Y_n}{\log\log n / n} = 1$ almost surely with …

For any choice of $C_1,C_2,\theta$ with $\theta \in (0,1)$ and $0 < C_1 < C_2$ (not sure why you said $C_2 < 1$), there are infinitely many $N$ with at least $c\exp\Bigl(c(1-\theta)\frac{\log N}{\log …

Say that a theory $T\supseteq \mathsf{ZFC}$ is CCMA ("complete computable mod arithmetic") iff $T$ is computable but $T^+:=T\cup\mathsf{TA}$ is complete and consistent, where $\mathsf{TA}$ is true ari …

I would seriously consider the photographic technology suggested by Kevin Buzzard in the comments, if you happen to have a decent digital camera handy (and if you trust your drawing skills). Or, as P …

Aaron Lauda has a nice description using the package XY-pic here (Wayback Machine). There are commands that generate pieces of knots (such as crossings in various orientations), although I prefer jus …

Have a look at the knot program by Kodama: https://www.math.kobe-u.ac.jp/HOME/kodama/knot.html You can draw and manipulate knot diagrams using the mouse and there is an option to export the figures to …