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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.
![$ f \sqcap \bigsqcup S = \bigsqcup \langle f \sqcap \rangle^{\ast} S $](/files/tex/0a7e06f88b6cd4667f7fa4b6f670b57cfa795155.png)
![$ f $](/files/tex/43374150a8a220f67049937b9790b7d28eb17fb9.png)
![$ S $](/files/tex/d2b76a0ee5465d3e3ecc846c8e3d632edd8b2bbf.png)
Keywords: distributivity; principal funcoid
Distributivity of a lattice of funcoids is not provable without axiom of choice ★
Author(s): Porton
Conjecture Distributivity of the lattice
of funcoids (for arbitrary sets
and
) is not provable in ZF (without axiom of choice).
![$ \mathsf{FCD}(A;B) $](/files/tex/d051d7da40c4a6b1d4234c0f74689d1bc7c994f1.png)
![$ A $](/files/tex/7a8d9782350e8eb5a84c149576d83160492cbdd3.png)
![$ B $](/files/tex/4369e4eb2b0938fb27436a8c4f4a062f83d4d49e.png)
A similar conjecture:
Conjecture
for arbitrary filters
and
on a powerset cannot be proved in ZF (without axiom of choice).
![$ a\setminus^{\ast} b = a\#b $](/files/tex/c6fc3b6da0655ddeaeffe670703a33edcb4650f6.png)
![$ a $](/files/tex/b1d91efbd5571a84788303f1137fb33fe82c43e2.png)
![$ b $](/files/tex/b94226d9717591da8122ae1467eda72a0f35d810.png)
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
Keywords: distributive; distributivity; funcoid; functor; inward reloid; reloid
Distributivity of outward reloid over composition of funcoids ★★
Author(s): Porton
Keywords: distributive; distributivity; funcoid; functor; outward reloid; reloid
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