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Showing 1 to 20 of 21 for “"boolean algebras"”.
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AN INTRODUCTION TO BOOLEAN ALGEBRAS
<p>This thesis discusses the topic of Boolean algebras. In order to build intuitive understanding of the topic, research began with the investigation of Boolean algebras in the area of Abstract Algebra. The content of this initial research used a particular notation. The ideas of partially ordered …
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The theory of commuting Boolean algebras
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 1997.
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Precipitous Ideals on Cbas (Complete Boolean Algebras)
… of the thesis is precipitous ideals on complete Boolean algebras (abbr. cBas) which are generalizations of precipitous ideals on power sets introduced by Jech and Prikry.
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FINITELY ADDITIVE MEASURES ON TOPOLOGICAL SPACES AND BOOLEAN ALGEBRAS
… o each other. The relation between charges on Boolean algebras and the induced measures on their Stone spaces is mentioned in this chapter. We also show that for any charge algebra, there exists a compact zero-dimensional space such that its charge algebra is isomorphic to the given charge …
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Some observations and results concerning submeasures on Boolean algebras
We investigate submeasures on Boolean algebras in the context of Maharam's problem and its solution. We generalise results that were originally proved for measures, to cases where additivity is not present. We investigate Talagrand's construction of a pathological exhaustive submeasure, attempting …
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Orderings and Boolean algebras not isomorphic to recursive ones
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 1967.
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Relationships Between Post and Boolean Algebras With Application to Multi-Valued Switching Theory
Made available in DSpace on 2014-12-10T20:13:30Z (GMT). No. of bitstreams: 1 7207111.pdf: 3414848 bytes, checksum: e1aabe57a6941db1c153e3c01cf9c182 (MD5) Previous issue date: 1971
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Sharp and Unsharp Structures. A Unifying Framework for Algebraic Logic
… the categorical equivalence between (indexed) Boolean algebras and regular double Stone algebras. Despite their strong categorical relation, distinct model-theoretic aspects are identified. However, their structural theories demonstrate a cohesive treatment, preserving significant elementary …
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Algebraic aspects of propositional logic
… We start by considering the category Bool of Boolean algebras, the algebraic counterpart of classical propositional logic. We provide an algebraic definition of theories and models of classical logic and provide algebraic algorithms to determine whether a chosen formula is a theorem of a given …
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Amalgamation in varieties of algebras
… Examples of varieties include many classes of algebras such as groups, semigroups, lattices and Boolean algebras. In 1927, O. Schreier showed that for any set of extensions of a given group, there is another extension of that group that in some sense contains all other extensions in the set. …
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Topics in combinatorics and combinatorial algorithms
… for several classes of posets, such as the Boolean algebras. The behavior of interval number under poset operations is studied and so are one-point removal theorems. Asymptotic bounds on the interval number of almost every poset are derived, as well as results concerning the computational …
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Generating finite integral relation algebras
Relation algebras and categories of relations in particular have proven to be extremely useful as a fundamental tool in mathematics and computer science. Since relation algebras are Boolean algebras with some well-behaved operations, every such algebra provides an atom structure, i.e., a relational …
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Applications of Homological Algebra to Equational Theories
… that some equational theories such as groups or Boolean algebras can be defined by fewer equational axioms than the original axioms. However, it is not easy to determine if a given set of axioms is the smallest or not. Malbos and Mimram investigated a general method to find a lower bound of the …
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Modal and Relevance Logics for Qualitative Spatial Reasoning
… to obtain a logic capable of reasoning about Boolean algebras i.e., the mereological aspect of QSR. Then, we extended the logic further by adding modal logic operators in order to reason about topological contact i.e., the topological aspect of QSR. Thus, we name this logic Modal Relevance …
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Finite Geometry and Computer Algebra, with Applications
… spaces with other areas, especially with boolean algebras and exterior algebras, and at how our results can determine various designs and codes. We also look at an example of how finite geometry relates to the algebra of Octonions, and finally we will see how a set of polynomial equations …
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Boolean-Valued Models and Their Applications
Boolean-valued models generalize classical two-valued models by allowing arbitrary complete Boolean algebras as value ranges. The goal of my dissertation is to study Boolean-valued models and explore their philosophical and mathematical applications. In Chapter 1, I build a robust theory of …
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Boolean ultrapowers
The Boolean ultrapower construction is a generalisation of the ordinary ultrapower construction in that an arbitrary complete Boolean algebra replaces the customary powerset Boolean algebra. B. Koppelberg and S. Koppelberg [1976] show that the class of ordinary ultrapowers is properly contained in …
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A CATEGORICAL-ALGEBRAIC EXPLORATION OF MODELS FOR MANY-VALUED LOGIC
… the structures of lattice-ordered groups and MV-algebras, which are used in modeling logic with many truth values. In the first part, we show that the semi-abelian category of lattice-ordered groups satisfies several important properties, namely it is fiber-wise algebraically cartesian closed, …
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Approaches to reflective hulls of subcategories
… and Tholen 1988: Is the category of complete Boolean algebras an intersection of reflective subcategories of the category of frames?
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Problems in extremal combinatorics
We consider a variety of problems in extremal graph and set theory. Given a property $\Gamma$ and a family of sets ${\mathcal F}$, let $f({\mathcal F},\Gamma)$ be the size of the largest subfamily of ${\mathcal F}$ having property $\Gamma$. Let $f(m,\Gamma)$ be the minimum of $f({\mathcal …
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