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A construction of Boolean algebras from first-order structures

1993
*
Annals of Pure and Applied Logic
*

.,

doi:10.1016/0168-0072(93)90095-u
fatcat:kmf223ldmnh4bdllpveitele54
*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*. ...##
###
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]

2020
*
Lecture Notes in Computer Science
*

This involves using function liftings to implement some aspects

doi:10.1007/978-3-030-51054-1_14
fatcat:7oikixg6rrdhdeiwl3j7k64fty
*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. ...##
###
A Cook's tour of duality in logic: from quantifiers, through Vietoris, to measures
[article]

2020
*
arXiv
*
pre-print

In particular, we focus on the use

arXiv:2007.15415v1
fatcat:d7fs2d66tffg3m7o5ob6xz6tt4
*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*. ...##
###
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

2010
*
Central European Journal of Mathematics
*

We prove

doi:10.2478/s11533-010-0014-7
fatcat:kkwhax72szc55dsey7xzeehcbi
*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 ...##
###
Constructive version of Boolean algebra

2012
*
Logic Journal of the IGPL
*

The notion

doi:10.1093/jigpal/jzs021
fatcat:2gwifvemcffd5bygnzhjyeqmcm
*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*. ...##
###
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

2004
*
Foundations of physics
*

The .scheme leads to

doi:10.1023/b:foop.0000037623.08379.df
fatcat:3qcmoz3y7vhifagbaitlysnoba
*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. ...##
###
The countable existentially closed pseudocomplemented semilattice

2017
*
Archive for Mathematical Logic
*

Let K be

doi:10.1007/s00153-017-0527-x
fatcat:mrn3biki7vbx3lui65kcs4um3i
*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. ...##
###
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]

2007
*
Lecture Notes in Computer Science
*

We try to make

doi:10.1007/978-3-540-75939-3_8
fatcat:oc6ddifeubch3errgym5zryw4a
*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. ...##
###
Boolean powers, recursive models, and the Horn theory of a structure

1984
*
Pacific Journal of Mathematics
*

This paper concerns the

doi:10.2140/pjm.1984.114.207
fatcat:grpdbq2c2rbrhavdf4dxt4wxji
*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. ...##
###
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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