A connection between algebraic structures and propositional logic

dc.contributor.advisor Cáceres, Luis F. Ortiz-Hernández, Wanda College of Arts and Sciences - Sciences en_US
dc.contributor.committee Castellini, Gabriele
dc.contributor.committee Oltikar, Balchandra
dc.contributor.department Department of Mathematics en_US
dc.contributor.representative Macchiavell, Raúl 2019-04-15T15:50:42Z 2019-04-15T15:50:42Z 2006
dc.description.abstract 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. en_US
dc.description.abstract En este proyecto se estudió la relación entre la lógica proposicional utilizando teorías y modelos, y estructuras algebraicas como: grupos, anillos, retículos, R-módulos y álgebras, incluyendo álgebras de Boole. De Cáceres [1] tenemos que dado un anillo R, existe una correspondencia uno a uno entre los ideales de R y los modelos asociados a la teoría sentencial T(R). Utilizando un procedimiento similar se demostró que dado un grupo G y la teoría sentencial asociada, T(G), existe una correspondencia uno a uno entre los subgrupos de G y los modelos asociados con la teoría, T(G). Para los retículos, L, y las álgebras de Boole, B, se presentaron varios resultados y propiedades. Además, se establecieron sus teorías sentenciales, T(L) y T(B), respectivamente. Varios ejemplos y contra ejemplos concretos se presentaron para reforzar los resultados establecidos. Para algunas estructuras se estudió la cardinalidad de sus teorías proposicionales correspondientes y se estableció una fórmula para su computación. en_US
dc.description.graduationYear 2006 en_US
dc.language.iso English en_US
dc.rights.holder (c) 2006 Wanda Ortiz-Hernández en_US
dc.rights.license All rights reserved en_US
dc.subject Algebraic structures en_US
dc.subject Propositional logic en_US
dc.title A connection between algebraic structures and propositional logic en_US
dc.type Thesis en_US
dspace.entity.type Publication Pure Mathematics en_US M.S. en_US
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