Generalized Boolean models and classical predicate logic
Tomáš Lávička · Digital Repository (National Repository of Grey Literature) · 2013
This bachelor thesis is dealing with complete Boolean algebras and its use in semantics of first-order predicate logic. This thesis has two main goals, at first it is to show that every Boolean al- gebra can be extended to a complete Boolean algebra such that the former Boolean algebra is its dense subalgebra. This theorem is proved using topological construction. Afterwards, in the sec- ond part, we define semantics for first-order predicate logic with respect to complete Boolean algebras, which includes introduc- tion of the Boolean-valued model. Then we prove completeness theorem with respect to all complete Boolean algebras. The the- orem is proven using ultrafilters on Boolean algebras. Keywords: Boolean algebras, complete Boolean algebras, clas- sical logic.