Boolean algebra approximations

Boolean Algebra Approximations

Knight and Stob proved that every low4 Boolean algebra is 0-isomorphic to a computable one. Furthermore, for n = 1, 2, 3, 4, every lown Boolean algebra is 0-isomorphic to a computable one. We show that this is not true for n = 5: there is a low5 Boolean algebra that is not 0-isomorphic to any computable Boolean algebra. It is worth remarking that, because of the machinery developed, the proof u...

Ternary Boolean Algebra

Free Boolean Algebra

This theory defines a type constructor representing the free Boolean algebra over a set of generators. Values of type (α)formula represent propositional formulas with uninterpreted variables from type α, ordered by implication. In addition to all the standard Boolean algebra operations, the library also provides a function for building homomorphisms to any other Boolean algebra type. 1 Free Boo...

Single Axioms for Boolean Algebra

Explicit single axioms are presented for Boolean algebra in terms of (1) the Sheffer stroke; (2) disjunction and negation; (3) disjunction, conjunction, and negation; and (4) disjunction, conjunction, negation, 0, and 1. It was previously known that single axioms exist for these systems, but the procedures to generate them are exponential, producing huge equations. Automated deduction technique...

Boolean Algebra and the Yijing

There would seem to be a significant degree of interest in the Yi Jing from computer literate people. The number of web sites devoted to the changes is substantial (see the web site listed as [ICh98] in Section 7 for a comprehensive selection of crossreferences) and there are a wide range of Yi Jing consultation programs available, as freeware, shareware and commercial software. There is also a...