منابع مشابه
Boolean Algebras in Visser Algebras
We generalize the double negation construction of Boolean algebras in Heyting algebras, to a double negation construction of the same in Visser algebras (also known as basic algebras). This result allows us to generalize Glivenko’s Theorem from intuitionistic propositional logic and Heyting algebras to Visser’s basic propositional logic and Visser algebras. Mathematics Subject Classification: P...
متن کاملImaginaries in Boolean algebras
Given an infinite Boolean algebra B, we find a natural class of ∅-definable equivalence relations EB such that every imaginary element from B is interdefinable with an element from a sort determined by some equivalence relation from EB . It follows that B together with the family of sorts determined by EB admits elimination of imaginaries in a suitable multisorted language. The paper generalize...
متن کاملRobbins Algebras vs. Boolean Algebras
In the early 1930s, Huntington proposed several axiom systems for Boolean algebras. Robbins slightly changed one of them and asked if the resulted system is still a basis for variety of Boolean algebras. The solution (afirmative answer) was given in 1996 by McCune with the help of automated theorem prover EQP/OTTER. Some simplified and restucturized versions of this proof are known. In our vers...
متن کاملIrredundant Sets in Boolean Algebras
It is shown that every uncountable Boolean algebra A contains an uncountable subset / such that no a of / is in the subalgebra generated by I\{a} using an additional axiom of set theory. It is also shown that a use of some such axiom is necessary. A subset / of a Boolean algebra A is irredundant if no proper subset of / generates the same subalgebra as /, or equivalently, if no a of / is in the...
متن کاملBoolean Algebras in Algebraic Topology
The appearance of the complete Heyting algebra in the realm of Algebraic Topology is the main topic of the paper.
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ژورنال
عنوان ژورنال: Journal of Pure and Applied Algebra
سال: 1990
ISSN: 0022-4049
DOI: 10.1016/0022-4049(90)90132-2