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

Author(s): Porton

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).

A similar conjecture:

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).

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

Posted by porton
updated August 24th, 2013
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