# Distributivity of a lattice of funcoids is not provable without axiom of choice (Solved)

 Importance: Low ✭
 Author(s): Porton, Victor
 Subject: Topology
 Keywords: axiom of choice distributive lattice distributivity funcoid reverse math reverse mathematics ZF ZFC
 Posted by: porton on: August 24th, 2013
 Solved by: Todd Trimble
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.

## Bibliography

The blog post where the conjecture have been introduced

* indicates original appearance(s) of problem.