A Heyting algebra is a bounded lattice 
equipped with a binary operation 
such that 
iff 
for all 
. Every Heyting algebra is a distributive
lattice. negation is defined by 
. Unlike in a Boolean
algebra, the law of the excluded middle 
need not hold. A Heyting
algebra is a Boolean algebra exactly when this
identity holds for every 
.
Heyting algebras give the algebraic semantics of intuitionistic logic. For example, the open sets of a topological
space 
form a Heyting algebra, with
 |
Here 
denotes the interior.
The free Heyting algebra 
on two generators has a concrete representation due to Bellissima
(1986). Ye and Xu (2026) use this representation to claim that 
cannot be the Heyting algebra 
of subterminal
objects of any topos 
. Their argument constructs an upward-closed set
outside 
that would be definable as a global proposition if
such a topos existed. They also rule out any Heyting algebra
having 
as the image of a surjective homomorphism. The claims
have not received independent review. Ye and Xu (2026) state that ChatGPT 5.6 Sol
helped obtain the mathematical results but do not identify specific contributions.
