arXiv · 0705.0504
We show that several classical Ramseyan statements, and a forcing statement, are each equivalent to having Rothberger's property in all finite powers.
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Marion Scheepers. 2007-10-23. Rothberger's property in finite powers. https://arxiv.org/abs/0705.0504
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Inspired by a statement about Extended Frege proof systems by Jain and Jin (FOCS 2022) we prove that: - there is a p-time binary relation $\approx$ between circuits that implies their logical equivalence, - if the equivalence $C \equiv D$ has an Extended Frege or a Circuit Frege proof with $k$ steps then there is a chain of circuits $E_i$ $$ C = E_0 \approx \dots \approx E_t = D $$ with $t \le O(k \log k)$, and the total size of the chain is bounded above by $(k+|C|+|D|)^{O(1)}$.
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