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A construction of Boolean algebras from first-order structures

Sabine Koppelberg
1993 Annals of Pure and Applied Logic  
., 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  
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]

Walter Guttmann
2020 Lecture Notes in Computer Science  
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]

Mai Gehrke, Tomas Jakl, Luca Reggio
2020 arXiv   pre-print
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  
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  
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

Olivier Finkel, Stevo Todorčević
2010 Central European Journal of Mathematics  
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

F. Ciraulo, M. E. Maietti, P. Toto
2012 Logic Journal of the IGPL  
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  
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

Elias Zafiris
2004 Foundations of physics  
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

Joël Adler
2017 Archive for Mathematical Logic  
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  
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]

Costas A. Drossos, Panagis Karazeris
2007 Lecture Notes in Computer Science  
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

George Nelson
1984 Pacific Journal of Mathematics  
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  
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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