I am posting here the nice slides on this topic made by Ian Cavey, Christian Sprague, and Mac Stannard. The slides are meant for a presentation of about 20 minutes.
A kind of library
Andrés E. Caicedo
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- Answer by Andrés E. Caicedo for Well known theorems that have not been proved
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- Answer by Andrés E. Caicedo for The Erdős-Turán conjecture or the Erdős' conjecture?
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- Answer by Andrés E. Caicedo for What is the cardinality of $A \times \mathbb N$ if $\left \lvert A \right \rvert \geq \aleph_0\ $?
- Answer by Andrés E. Caicedo for Any partition of an at most countable set has a set of representatives.
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- Answer by Andrés E. Caicedo for $\beta > 0$ and $\alpha \cdot \beta = \beta \implies \alpha ^{\omega} \leq \beta$
- Does $|X|^m\cdot n^{|X|}\le (n+m)^{|X|}$ hold without choice?
- Answer by Andrés E. Caicedo for Transfinite derivatives
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A kind of library 
[…] I met Ian Cavey, an undergraduate at Boise State, about a year ago. He took my Communication in the mathematical sciences course. It was a pleasure to have him as a student. (You can see the slides of one of his group projects here.) […]