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In this article we investigate the notion and basic properties of Boolean algebras and prove the Stones representation theorem. The relations of Boolean algebras to logic and to set theory will be studied and, in particular, a neat proof of completeness theorem in propositional logic will be given using Stones theorem from Boolean algebra.
The article is a study of two algebraic structures, the `contrapositionally complemented pseudo-Boolean algebra (ccpBa) and `contrapositionally $vee$ complemented pseudo-Boolean algebra (c$vee$cpBa). The algebras have recently been obtained from a to
Boolean-type algebra (BTA) is investigated. A BTA is decomposed into Boolean-type lattice (BTL) and a complementation algebra (CA). When the object set is finite, the matrix expressions of BTL and CA (and then BTA) are presented. The construction and
We present a new approach to ternary Boolean algebras in which negation is derived from the ternary operation. The key aspect is the replacement of complete commutativity by other axioms that do not require the ternary operation to be symmetric.
Let 2<nleq l<m< omega. Let L_n denote first order logic restricted to the first n variables. We show that the omitting types theorem fails dramatically for the n--variable fragments of first order logic with respect to clique guarded semantics, and f
Recent advances in manipulating single electron spins in quantum dots have brought us close to the realization of classical logic gates based on representing binary bits in spin polarizations of single electrons. Here, we show that a linear array of