THE FINE STRUCTURE OF THE MEDVEDEV LATTICE AND THE PARTIAL DEGREES.
Item
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Title
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THE FINE STRUCTURE OF THE MEDVEDEV LATTICE AND THE PARTIAL DEGREES.
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Identifier
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AAI8801764
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identifier
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8801764
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Creator
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SORBI, ANDREA.
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Contributor
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Robert A. Di Paola
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Date
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1987
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Language
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English
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Publisher
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City University of New York.
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Subject
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Mathematics
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Abstract
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We investigate the Medvedev lattice of degrees of difficulty, as well as the Mucnick and the Dyment lattices. Relationships between these lattices in terms of homomorphisms are discussed. It is known that these lattices are Brouwer algebras; we show that the Mucnick lattice is also a Heyting algebra, whereas the Medvedev and the Dyment lattices are not. Chapter I contains also a thorough investigation of the algebraic structure of the Mucnick lattice and of the properties of the degrees of enumerability. Several sublattices of the Medvedev lattice are introduced, which turn out to be of some logical interest: for example the sublattice consisting of finite degrees of difficulty is an intuitionistic diagonalizable algebra.;In Chapter II we characterize the finite Heyting algebras and the finite Brouwer algebras which are embeddable in the Mucnick lattice; we prove also that a certain class of Brouwer algebras is embeddable in the Medvedev and the Dyment lattices; these results enable us to determine the intermediate logics corresponding to these lattices. The second part of Chapter II is devoted to the study of filters and ideals and the corresponding quotient lattices. Embedding theorems are proved, with some consequences in terms of intermediate logics.;Chapter III contains several results about the partial degrees, which are used to investigate the algebraic structure of some of the previous quotient lattices.
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Type
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dissertation
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Source
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PQT Legacy CUNY.xlsx
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degree
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Ph.D.
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Program
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Mathematics
