Geodesic
Symmetric Boolean Algebras
Acta mathematica Universitatis Comenianae, Tome 79 (2010) no. 2 
R. Díaz; M. Rivas. Symmetric Boolean Algebras. Acta mathematica Universitatis Comenianae, Tome 79 (2010) no. 2. http://geodesic.mathdoc.fr/item/AMUC_2010_79_2_a3/
@article{AMUC_2010_79_2_a3,
     author = {R. D{\'\i}az and M. Rivas},
     title = {Symmetric {Boolean} {Algebras}},
     journal = {Acta mathematica Universitatis Comenianae},
     year = {2010},
     volume = {79},
     number = {2},
     url = {http://geodesic.mathdoc.fr/item/AMUC_2010_79_2_a3/}
}
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JO  - Acta mathematica Universitatis Comenianae
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Voir la notice de l'article provenant de la source Comenius University

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.