**Conjecture**Distributivity of the lattice of funcoids (for arbitrary sets and ) is not provable in ZF (without axiom of choice).

A similar conjecture:

**Conjecture**for arbitrary filters and 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.