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Symmetric Boolean Algebras
R. Díaz and M. Rivas
Received: March 31, 2009; Accepted: October 12, 2009
Abstract. In order to study Boolean algebras in the category of vector spaces we introduce a prop whose algebras in set are Boolean algebras. A probabilistic logical interpretation for linear Boolean algebras is provided. An advantage of defining Boolean algebras in the linear category is that we are able to study its symmetric powers. We give explicit formulae for products in symmetric and cyclic Boolean algebras of various dimensions and formulate symmetric forms of the inclusion-exclusion principle.
Keywords: Boolean algebras; combinatorics; probabilistic logic.
AMS Subject classification: Primary: 06E99, 06A06, 03B48
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