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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

Constructive version of Boolean algebra [article]

Francesco Ciraulo, Maria Emilia Maietti, Paola Toto
2012 arXiv   pre-print
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.  ... 
arXiv:1203.4997v1 fatcat:e5t57plw3vexzgd7dxhnrtcxjm

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

Valdis Berzins
1994 ACM Transactions on Programming Languages and Systems  
Acknowledgement The author would like to thank Mike Mislove for kindly communicating that nondistributivity 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  ... 
doi:10.1145/197320.197403 fatcat:4x25r6lo7jbn3lprxq5qwt73gu

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]

Baofeng Wu, Jia Zheng
2013 arXiv   pre-print
In this correspondence, an equivalent definition 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.  ... 
arXiv:1305.5919v1 fatcat:ilnkzeternegdj24k5d5nknlhi

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

William Hanf
1975 Bulletin of the American Mathematical Society  
It is shown that every recursively enumerable 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.  ... 
doi:10.1090/s0002-9904-1975-13747-5 fatcat:a4n2fwtf7jeo7jvkx2im3fauoi

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

Rod Downey, Carl G. Jockusch
1999 Journal of Symbolic Logic (JSL)  
This extends a result 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] .  ... 
doi:10.2307/2586749 fatcat:cr5syg2gfbgildfcsynmabchai

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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