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A construction of Boolean algebras from first-order structures
1993
Annals of Pure and Applied Logic
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., A construction of Boolean algebras from first-order structures, ...
We give a construction assigning classes of Boolean algebras to first-order theories; several classes of Boolean algebras considered previously in the literature can be thus obtained. ...
The class of all Boolean algebras. Let _Y = { +, e, -, 0, l} be the language of Boolean algebras, T any first-order axiomatization of the theory of Boolean algebras. ...
doi:10.1016/0168-0072(93)90095-u
fatcat:kmf223ldmnh4bdllpveitele54
Page 4748 of Mathematical Reviews Vol. , Issue 98H
[page]
1998
Mathematical Reviews
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A countable first-order structure # is constructed such that for every set of integers XY , X is nonrecursive iff there is a presentation of @ which is recursive in X. ...
The third chapter, which is the longest one, deals with construc- tive Boolean algebras and with constructibility in linear orders and Boolean algebras. ...
Reasoning About Algebraic Structures with Implicit Carriers in Isabelle/HOL
[chapter]
2020
Lecture Notes in Computer Science
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This involves using function liftings to implement some aspects of dependent types and using embeddings of algebras to inherit theorems. We also formalise a theory of filters based on partial orders. ...
The development requires extensive reasoning about algebraic structures in addition to reasoning in algebraic structures. ...
Constructing a Triple from a Stone Algebra The first set of results concerns the construction of a triple from a Stone algebra S. Specifically, we show: 1. ...
doi:10.1007/978-3-030-51054-1_14
fatcat:7oikixg6rrdhdeiwl3j7k64fty
A Cook's tour of duality in logic: from quantifiers, through Vietoris, to measures
[article]
2020
arXiv
pre-print
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In particular, we focus on the use of (i) topological duality methods to solve problems in logic and computer science; (ii) category theory and, more particularly, free (and co-free) constructions; (iii ...
) these tools to unify the 'power' and 'structure' strands in computer science. ...
First, we focus on existential quantification in first-order logic over arbitrary structures. Then, on semiring and probabilistic quantifiers in first-order logic over finite structures. ...
arXiv:2007.15415v1
fatcat:d7fs2d66tffg3m7o5ob6xz6tt4
Page 878 of Mathematical Reviews Vol. 46, Issue 4
[page]
1973
Mathematical Reviews
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Let L(r) be a first-order language of type 7 and let X(7) _ be the class of all structures of type 7. ...
The author
defines the notion of a completion of a Boolean algebra
with partially additive operators and proves (Theorem 8)
that if B is a completion of a completely partially additive
Boolean algebra ...
Page 6179 of Mathematical Reviews Vol. , Issue 90K
[page]
1990
Mathematical Reviews
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In Chapter 27 Jech briefly discusses the relationship between properties of a structure in a Boolean-valued model of set the- ory and its properties as a Boolean-valued structure, i.e., as the structure ...
Invariants for countable algebras
06 ORDER, LATTICES, ORDERED ALGEBRAIC STRUCTURES
90k:06004
(and, dually, for metrizable Boolean spaces), including the classi- fication by J. ...
The isomorphism relation between tree-automatic Structures
2010
Central European Journal of Mathematics
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We prove first that the isomorphism relation for ω-tree-automatic boolean algebras (respectively, partial orders, rings, commutative rings, non commutative rings, non commutative groups, nilpotent groups ...
of class n >1) is neither a Σ_2^1-set nor a Π_2^1-set. ...
We are indebted to Anatole Khélif who was generously sharing with us his expertise about unitriangular groups and to the anonymous referees for very useful comments on a preliminary version of this paper ...
doi:10.2478/s11533-010-0014-7
fatcat:kkwhax72szc55dsey7xzeehcbi
Constructive version of Boolean algebra
2012
Logic Journal of the IGPL
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The notion of overlap algebra introduced by G. Sambin provides a constructive version of complete Boolean algebra. ...
Then, we generalize the concept of overlap algebra and overlap morphism in various ways to provide constructive versions of the category of Boolean algebras with maps preserving arbitrary existing joins ...
Acknowledgements We express our gratitude to Giovanni Sambin and Steve Vickers for very interesting discussions about overlap algebras and their interplay with Boolean algebras. ...
doi:10.1093/jigpal/jzs021
fatcat:2gwifvemcffd5bygnzhjyeqmcm
Page 595 of Mathematical Reviews Vol. 50, Issue 3
[page]
1975
Mathematical Reviews
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In the first part, the
author gives a construction to obtain any topological algebra as a
first order structure, (For example, let °=<A, f> be a topological
algebra and let U,, i € A, be a basis for the ...
field of p-adic numbers) field and any infinite strongly constructive Boolean algebra have a proper strongly constructive elementary extension. ...
Quantum Event Structures from the Perspective of Grothendieck Topoi
2004
Foundations of physics
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The .scheme leads to a sheaf theoretical representation of Quantum structure in terms of variation taking place over epinuirphic families of Boolean reference frames ...
We show that the established adjunction can be transformed to a categorical equivak'nie if the base category of Boolean event algebras, defining variation, is endowed with a suitable Grothendieck topology ...
ACKNOWLEDGMENTS The author is member of the EDGE Research Training Network HPRN-CT-2000-UOlOI. supported by the European Human Potential Programme. ...
doi:10.1023/b:foop.0000037623.08379.df
fatcat:3qcmoz3y7vhifagbaitlysnoba
The countable existentially closed pseudocomplemented semilattice
2017
Archive for Mathematical Logic
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Let K be a class of first-order structures of the same (finitary) type, and L K a first-order language suitable for K. ...
Let K be a class of first-order structures of the same (finitary) type, and L K a first-order language suitable for K. ...
doi:10.1007/s00153-017-0527-x
fatcat:mrn3biki7vbx3lui65kcs4um3i
Page 1352 of Mathematical Reviews Vol. , Issue 85d
[page]
1985
Mathematical Reviews
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The interpretation of G in A(R) is constructed first. ...
The paper is self-contained
ORDER, LATTICES, ORDERED ALGEBRAIC STRUCTURES
1352
except for two results from recursion theory, and thus in principle is accessible to those who are not specialists in ordered ...
A Note on Representing and Interpreting MV-Algebras
[chapter]
2007
Lecture Notes in Computer Science
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We try to make a distinction between the idea of representing and that of interpreting a mathematical structure. ...
Furthermore, we examine some preservation and functorial aspects of the Boolean power construction. 1991 Mathematics Subject Classification. 06D35,03B50,03c20, 03C90. ...
The existence of a huge amount of nonstandard models implies that the structure of MV-algebras (alongside with many other first-order structures) can have many nonstandard interpretations. ...
doi:10.1007/978-3-540-75939-3_8
fatcat:oc6ddifeubch3errgym5zryw4a
Boolean powers, recursive models, and the Horn theory of a structure
1984
Pacific Journal of Mathematics
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This paper concerns the algebraic constructions of Boolean powers and bounded Boolean powers of structures 3ί for an arbitrary first-order language. ...
The notion of ^-separating is used to improve results about the logic of reduced power structures. For 2ί recursive we construct recursive models of the theory of each reduced power of 2ί. ...
We also introduce a standard language construction which allows one to 207 obtain ^-separating structures % f with algebraic language L f from ^-separating structures 21 with first-order language L. ...
doi:10.2140/pjm.1984.114.207
fatcat:grpdbq2c2rbrhavdf4dxt4wxji
Page 5157 of Mathematical Reviews Vol. , Issue 2004g
[page]
2004
Mathematical Reviews
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This paper gives two criteria for homogeneity of a Boolean algebra, and three constructions of first countable linearly ordered Boolean spaces with different cardinal invariants. ...
is of type A” and/or “t is a proof of A”. Rules of inference of HL are all represented as rules of term formation, but some terms of first order formula type may not be first order proofs. ...
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