### One more conjecture about provability without axiom of choice

I addition to this conjecture I formulate one more similar conjecture: Conjecture \$latex a\setminus^{\ast} b = a\#b\$ for arbitrary filters \$latex a\$ and \$latex b\$ on a powerset cannot be proved in ZF (without axiom of choice). Notation (where \$latex \mathfrak{F}\$ is…

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

Conjecture Distributivity of the lattice \$latex \mathsf{FCD}(A;B)\$ of funcoids (for arbitrary sets \$latex A\$ and \$latex B\$) is not provable in ZF (without axiom of choice). It is a remarkable conjecture, because it establishes connection between logic and a purely algebraic equation….