# reverse math

## Distributivity of a lattice of funcoids is not provable without axiom of choice ★

Author(s): Porton

**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).

Keywords: axiom of choice; distributive lattice; distributivity; funcoid; reverse math; reverse mathematics; ZF; ZFC