Recomm. for undergrads: no
Posted by: porton
on: August 24th, 2013
Solved by: Todd Trimble
Conjecture   Distributivity of the lattice $ \mathsf{FCD}(A;B) $ of funcoids (for arbitrary sets $ A $ and $ B $) is not provable in ZF (without axiom of choice).

A similar conjecture:

Conjecture   $ a\setminus^{\ast} b = a\#b $ for arbitrary filters $ a $ and $ b $ on a powerset cannot be proved in ZF (without axiom of choice).

See this blog post for a rationale of this conjecture.

See here for used notation.

The first conjecture is shown false (that is a proof without AC exists) by Todd Trimble.

* indicates original appearance(s) of problem.


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