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### “Arithmetically diverse” infinite binary string

For $a,b \in \omega$ with $a > 0$, let $f_{a,b}: \omega\to\omega$ be defined by $n \mapsto an+b$. What is an example of an infinite binary string $b:\omega\to\{0,1\}$ with the following property? ...
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### A reform of logic to secure naive set theory? [closed]

Set-theoretic paradoxes noted by Russell and others led to attempts to produce a consistent set theory as a foundation for mathematics. (Stanford Encyclopedia of Philosophy. Inconsistent Mathematics) ...
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### Category theory and set theory: just a different language, or different foundation of mathematics?

This is a question to research mathematicians, as well as to those concerned with the history and philosophy of mathematics. I am asking for a reference. In order to make the reference request as ...
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### Homotopy group action and equivariant cohomology theories

Many of the introductory notes on generalized equivariant cohomology theories assume that one is working over the category of $G$-spaces or $G$-spectra. However, one thing that concerns me is that the ...
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### Does category of finitely generated torsion $G$-modules has enough injectives?

Let $G$ be a profinite group. Then the category of discrete $G$-modules have enough injectives. Now I have a category of finitely generated and torsion $G$-modules with continuous $G$-action. Does ...
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### Fourier transform on finite groups in characteristic $p>0$

Is there a Fourier theory for finite groups in characteristic $p>0$? Assume that $p$ divides the order $|G|$ of finite groups (or just work with $p$-groups), i.e., in a modular representation-...
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### Isometric embedding of the modular surface

Is there an isometric embedding of the modular surface $X(1)=PSL(2,\mathbb{Z})\backslash \,\mathbb{H}$ into the Euclidean 3-space? For all I know this may be an open problem but I am also curious if ...
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### Consequences of Gromov's Conjecture

In Peter Petersen words, Gromov Betti number estimate is considered one of the deepest and most beautiful results in Riemannian geometry; which asserts that Theorem (Gromov 1981). There is a constant ...
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### Behavior of invariants under reduction mod p

Let $R$ be a finitely generated $\mathbb{Z}$-algebra with an [edit: linear algebraic] action of $G(\mathbb{Z})$ where $G$ is a split simply-connected semisimple group. Then for any prime $p$ we have a ...
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### What is the best way to study Rational Homotopy Theory

I studied basic algebraic topology elements: fundamental group, higher homotopy groups, fibre bundles, homology groups, cohomology groups, obstruction theory, etc. I want to study Rational Homotopy ...