O zupełnych algebrach Heytinga

Speaker(s)

Konrad Zdanowski

Affiliation

UKSW

Language of the talk

Polish

Date

Oct. 30, 2026, 12:15 p.m.

Room

room 5450

Title in English

On complete Heyting algebras

Seminar

Seminar Semantics, Logic, Verification and its Applications

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This presentation is based upon a recent paper 
'Two applications of the point-free coderivative'
by Zoltan A. Kocsis

The abstract of this paper is

We present two new applications of Simmons' point-free Cantor-Bendixson
coderivative operator in intuitionistic logic. First, we use it to give
a simplified proof of the recent result of Xu and Ye that the free
Heyting algebra on two generators does not occur as the Heyting algebra
of subterminal objects in any elementary topos. Then we use it to prove
that complete Heyting algebra semantics is not strongly complete for
intuitionistic second-order propositional logic: semantic consequence
from an arbitrary set of assumptions does not coincide with ordinary
syntactic consequence.

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