# distributivity

## Infinite distributivity of meet over join for a principal funcoid ★★

Author(s): Porton

**Conjecture**for principal funcoid and a set of funcoids of appropriate sources and destinations.

Keywords: distributivity; principal funcoid

## 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

## Distributivity of inward reloid over composition of funcoids ★★

Author(s): Porton

**Conjecture**for any composable funcoids and .

Keywords: distributive; distributivity; funcoid; functor; inward reloid; reloid

## Distributivity of outward reloid over composition of funcoids ★★

Author(s): Porton

**Conjecture**for any composable funcoids and .

Keywords: distributive; distributivity; funcoid; functor; outward reloid; reloid