Ortiz-Hernández, Wanda

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A connection between algebraic structures and propositional logic
(2006) Ortiz-Hernández, Wanda; Cáceres, Luis F.; College of Arts and Sciences - Sciences; Castellini, Gabriele; Oltikar, Balchandra; Department of Mathematics; Macchiavell, Raúl
In this project, the relationship between propositional logic using theories and models, and algebraic structures, such as groups, rings, lattices, R-modules and algebras, including Boolean Algebras, has been studied. From Caceres [1], we have that given a ring R, a one to one correspondence exists between the ideals of R and the models associated with the sentential theory T(R). A similar approach was followed to show that given a group G, and the associated sentential theory T (G), a one to one correspondence exists between the subgroup of G and the models associated with the theory T(G). Several results were presented for lattice structures, L, and Boolean Algebras, B. Their associated sentential the- ories, T(L) and T(B), were also established. Concrete examples to support these results were presented and explained. For some structures, the cardinality of its corresponding propositional theory was studied and a formula for its calculation was established.