Hyper-MacNeille Completions of Heyting Algebras

A Heyting algebra is supplemented if each element a has dual pseudo-complement $$a^+$$ , and centrally supplement it central. We show that extension in the same variety of algebras as original. use this tool to investigate new type completion arising context algebraic proof theory, so-called hyper-MacNeille completion. MacNeille its extension. This provides an description algebra, allows development further properties completion, examples varieties are closed under completions. In particular, connections between Boolean products allow us any finitely generated