# Heyting

### Some articles on heyting:

Arend Heyting
... Arend Heyting ( May 9, 1898 – July 9, 1980) was a Dutch mathematician and logician ... Heyting gave the first formal development of intuitionistic logic in order to codify Brouwer's way of doing mathematics ... of Brouwer's name in the Brouwer–Heyting–Kolmogorov interpretation is largely honorific, as Brouwer was opposed in principle to the formalisation of ...
Heyting Algebra - Quotients
... Let H be a Heyting algebra, and let F ⊆ H ... If H is a Heyting algebra and F is a filter on H, we define a relation ∼ on H as follows we write x ∼ y whenever x → y and y → x both belong ... There is a unique Heyting algebra structure on H/F such that the canonical surjection pF H → H/F becomes a Heyting algebra morphism ...
Brouwer–Heyting–Kolmogorov Interpretation
... In mathematical logic, the Brouwer–Heyting–Kolmogorov interpretation, or BHK interpretation, of intuitionistic logic was proposed by L ... Brouwer, Arend Heyting and independently by Andrey Kolmogorov ...
Church's Thesis (constructive Mathematics)
... For example, Heyting arithmetic (HA) with CT as an addition axiom is able to disprove some instances of the law of the excluded middle ... However, Heyting arithmetic is equiconsistent with Peano arithmetic (PA) as well as with Heyting arithmetic plus Church's thesis ... either the law of the excluded middle or Church's thesis does not make Heyting arithmetic inconsistent, but adding both does ...
Heyting Arithmetic
... In mathematical logic, Heyting arithmetic (sometimes abbreviated HA) is an axiomatization of arithmetic in accordance with the philosophy of intuitionism (Troelstra 197318) ... It is named after Arend Heyting, who first proposed it ... Heyting arithmetic adopts the axioms of Peano arithmetic (PA), but uses intuitionistic logic as its rules of inference ...