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May 31, 2012 / porton

A difficulty on the way of my research

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.

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3 Comments

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  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.

    • porton / May 31 2012 19:26

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

  2. porton / May 31 2012 22:00

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

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