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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*. ...##
###
Constructive version of Boolean algebra
[article]

2012
*
arXiv
*
pre-print

The notion

arXiv:1203.4997v1
fatcat:e5t57plw3vexzgd7dxhnrtcxjm
*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 4748 of Mathematical Reviews Vol. , Issue 98H
[page]

1998
*
Mathematical Reviews
*

He investigates the spectrum

*of*al- gorithmic dimensions*of**Boolean**algebras*and looks at positive*Boolean**algebras*(quotient*algebras**of**constructive**Boolean*al- gebras by recursively enumerable ideals ... The third chapter, which is the longest one, deals with construc- tive*Boolean**algebras*and with*constructibility*in linear orders and*Boolean**algebras*. ...##
###
Page 3146 of Mathematical Reviews Vol. , Issue 2000e
[page]

2000
*
Mathematical Reviews
*

*Constructive*

*Boolean*

*algebras*with decidability conditions on ul- trafilters. (Problems

*of*effectiveness and complexity

*of*ultrafilters in

*constructive*

*Boolean*

*algebras*are studied.) 6. ... Restricted theories

*of*

*Boolean*

*algebras*. (This section studies

*constructive*

*Boolean*

*algebras*whose theories with n quantifiers are decidable, for n < w, and related problems.) 5. ...

##
###
Page 6069 of Mathematical Reviews Vol. , Issue 2001I
[page]

2001
*
Mathematical Reviews
*

We show that this second result is best possible by

*constructing*a computable*Boolean**algebra*@ which is isomorphic to the*Boolean**algebra*generated by the closed inter- vals*of*the rationals such that ... In particular, we introduce polynomial-time representations*of*three specific*Boolean**algebras*which play a key role in our main results, namely, the*Boolean**algebra**of*finite and cofinite subsets*of*the ...##
###
Page 8592 of Mathematical Reviews Vol. , Issue 2001M
[page]

2001
*
Mathematical Reviews
*

This is a ZFC result (improving an earlier result

*of*Rubin from a © principle). The*construction*uses pef theory. (2) There is a superatomic*Boolean**algebra*with fewer automor- phisms than elements. ... Four results in*Boolean**algebra*are presented. (1) There is a superatomic*Boolean**algebra*with fewer automor- phisms than endomorphisms. ...##
###
Software merge: semantics of combining changes to programs

1994
*
ACM Transactions on Programming Languages and Systems
*

Acknowledgement The author would like to thank Mike Mislove for kindly communicating that nondistributivity

doi:10.1145/197320.197403
fatcat:4x25r6lo7jbn3lprxq5qwt73gu
*of*the Egli-Milner power domain is part*of*the folklore*of*domain theory and to thank the referees ... This section reviews the basic properties*of**Boolean**algebras*and shows how to*construct*the*Boolean**algebras*for higher order function spaces. ... The current paper repairs the deficiencies in the*Boolean*function space*construction*, and introduces*Boolean**versions**of*an extended sum constructor, two*of*the three main power domain constructors, and ...##
###
Page 5157 of Mathematical Reviews Vol. , Issue 2004g
[page]

2004
*
Mathematical Reviews
*

the homogeneity

*of**Boolean**algebras*and*Boolean*spaces. ... 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. ...##
###
A remark on algebraic immunity of Boolean functions
[article]

2013
*
arXiv
*
pre-print

In this correspondence, an equivalent definition

arXiv:1305.5919v1
fatcat:ilnkzeternegdj24k5d5nknlhi
*of**algebraic*immunity*of**Boolean*functions is posed, which can clear up the confusion caused by the proof*of*optimal*algebraic*immunity*of*the Carlet-Feng ... function and some other functions*constructed*by virtue*of*Carlet and Feng's idea. ... As a result, the standard definition*of**algebraic*immunity*of**Boolean*functions can be modified to an equivalent*version*, which is given in Section 2. ...##
###
Page 1352 of Mathematical Reviews Vol. , Issue 85d
[page]

1985
*
Mathematical Reviews
*

The interpretation

*of*G in A(R) is*constructed*first. ... 854:06012 O6E*Boolean**algebras*See also 03067, 03123, 05135, 08010, 94018. Flaksmaler, Yu. aren, Jiirgen] Topological semifields and*Boolean**algebras*corresponding to them. ...##
###
The Boolean algebra of logic

1975
*
Bulletin of the American Mathematical Society
*

It is shown that every recursively enumerable

doi:10.1090/s0002-9904-1975-13747-5
fatcat:a4n2fwtf7jeo7jvkx2im3fauoi
*Boolean**algebra*is isomorphic to the*Boolean**algebra**of*sentences*of*some finitely axiomatizable theory. ... Another consequence is that there exists a finitely axiomatizable theory whose*Boolean**algebra**of*sentences has an ordered basis*of*type 0 where 0 is any*constructive*ordinal. ... It is shown that every recursively enumerable*Boolean**algebra*is isomorphic to the*Boolean**algebra**of*sentences*of*some finitely axiomatizable theory. ...##
###
Page 772 of Mathematical Reviews Vol. , Issue 97B
[page]

1997
*
Mathematical Reviews
*

Finally, Section 3 is an

*algebraic*application*of*general*constructions*to the explicit extension*of**Boolean*and Heyting*algebras*to complete ones with the preservation*of*all existing joins and meets. ... From the introduction: “Section | is a reconstruction*of*basic def- initions and facts concerning Heyting and*Boolean**algebras*in the framework*of*our*constructive*approach. ...##
###
Effective presentability of Boolean algebras of Cantor-Bendixson rank 1

1999
*
Journal of Symbolic Logic (JSL)
*

This extends a result

doi:10.2307/2586749
fatcat:cr5syg2gfbgildfcsynmabchai
*of*L. Feiner and is deduced from Feiner's result even though Feiner's*construction*yields a*Boolean**algebra**of*infinite Cantor-Bendixson rank. ... We show that there is a computable*Boolean**algebra*and a computably enumerable ideal I*of*such that the quotient*algebra*/I is*of*Cantor-Bendixson rank 1 and is not isomorphic to any computable*Boolean*...*Boolean**algebra*which is not isomorphic to any computable*Boolean**algebra*. A simplied*version**of*Feiner's proof is given by J . T h urber in [12, Corollary 3.4] . ...##
###
Page 1582 of Mathematical Reviews Vol. , Issue 2003C
[page]

2003
*
Mathematical Reviews
*

The notion

*of*tight «-filteredness*of*a*Boolean**algebra*is closely connected to projectivity: a*Boolean**algebra*is projective if and only if it is tightly No-filtered. ... He proves that complete*Boolean**algebras**of*size > &3 are not tightly &-filtered. ...##
###
Page 3450 of Mathematical Reviews Vol. , Issue 97F
[page]

1997
*
Mathematical Reviews
*

The

*Boolean*kernels*of*a soft*algebra*correspond to the neutral elements*of*the quotient*algebra*. ... In this paper we present the topological*version**of*the classical Stone representation theorem for*Boolean*hyperalgebras.” {For the entire collection see MR 97b:05001.} See also 03072, 68057. ...
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