ZF


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

Author(s): Porton

\begin{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). \end{conjecture}

A similar conjecture:

\begin{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). \end{conjecture}

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

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