The following conjecture seems trivial but I have a hard hour trying to prove it. I suspect I have a big difficulty on the course of my research.

Conjecture $\prod^{\mathsf{FCD}} a \not\asymp\prod^{\mathsf{FCD}} b \Leftrightarrow \forall i\in n : a_i \not\asymp b_i$ for every $n$-indexed (where $n$ is an arbitrary index set) families of filters $a$ and $b$.

See This Web page and specifically this draft article for the notation I use.

1. porton / May 31 2012 19:14

It seems I have found a proof. See a proof sketch (with minor errors) in this rough draft.

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• porton / May 31 2012 19:26

Well, there is an unfounded step in this proof. I keep trying to prove it.

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2. porton / May 31 2012 22:00

I give up. I am going to publish it as a conjecture.

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