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Title Davey, Brian A.: Dualisability in general and endodualisability in particular Author info Miroslav Haviar Author Haviar Miroslav 1965- (100%) UMBPF03 - Katedra matematiky
Source document MathSciNet : Mathematical Reviews on the web. online, MR1404951 (97h:08001), pp. [1-2]. - Providence : American Mathematical Society, 1997 Review document Dualisability in general and endodualisability in particular / Brian A. Davey. - New York : Dekker, 1996 Keywords algebra - algebra duality prirodzené recenzie - reviews Language English Country United States of America systematics 51 Public work category EDI No. of Archival Copy 43324 Catal.org. UKUMB###KHPV###BB301 - Univerzitná knižnica Univerzity Mateja Bela v Banskej Bystrici Database xpca - PUBLIKAČNÁ ČINNOSŤ 
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Title Davey, B. A.; Priestley, H. A.: Optimal natural dualities for varieties of Heyting algebras Author info Miroslav Haviar Author Haviar Miroslav 1965- (100%) UMBFP10 - Katedra matematiky
Source document MathSciNet : Mathematical Reviews on the web. online, MR1382168 (97f:06026), pp. [1-2]. - Providence : American Mathematical Society, 1997 Review document Optimal natural dualities for varieties of Heyting algebras / B. A. Davey, H. A. Priestley. - [Heidelberg] : Springer Netherlands, 1996 Keywords matematika - mathematics recenzie - reviews Language English Country United States of America systematics 51 Public work category EDI No. of Archival Copy 43327 Catal.org. BB301 - Univerzitná knižnica Univerzity Mateja Bela v Banskej Bystrici Database xpca - PUBLIKAČNÁ ČINNOSŤ 
article
Title Factor principal congruences and Boolean products in filtral varieties Author info Brian A. Davey, Miroslav Haviar Author Davey Brian A. (50%)
Co-authors Haviar Miroslav 1965- (50%) UMBFP10 - Katedra matematiky
Source document Algebra Universalis. Vol. 85, no. 19 (2024), pp. 1-23. - Basel : Springer Nature Switzerland AG, 2024 Keywords algebra - algebra Boolean algebra kongruencie Form. Descr. články - journal articles Language English Country Switzerland Annotation Motivated by Haviar and Ploščica's 2021 characterisation of Boolean products of simple De Morgan algebras, we investigate Boolean products of simple algebras in filtral varieties. We provide two main theorems. The first yields Werner's Boolean-product representation of algebras in a discriminator variety as an immediate application. The second, which applies to algebras in which the top congruence is compact, yields a generalisation of the Haviar–Ploščcica result to semisimple varieties of Ockham algebras. The property of having factor principal congruences is fundamental to both theorems. While major parts of our general theorems can be derived from results in the literature, we offer new, self-contained and essentially elementary proofs. URL https://link.springer.com/article/10.1007/s00012-024-00846-8 Public work category ADC No. of Archival Copy 54297 Catal.org. BB301 - Univerzitná knižnica Univerzity Mateja Bela v Banskej Bystrici Database xpca - PUBLIKAČNÁ ČINNOSŤ References PERIODIKÁ-Súborný záznam periodika article
Title Expanding Belnap 2: the dual category in depth Author info Andrew P. K. Craig, Brian A. Davey, Miroslav Haviar Author Craig Andrew, P. K. (34%)
Co-authors Davey Brian A. (33%)
Haviar Miroslav 1965- (33%) UMBFP10 - Katedra matematiky
Source document Categories and General Algebraic Structures with Applications. Vol. 17, no 1 (2022), pp. 47-83. - Teherán : Shahid Beheshti University, 2022 Keywords bizväzy - bilattices prirodzená dualita Priestleyovská dualita Form. Descr. články - journal articles Language English Country Iran Annotation Bizväzy poskytujú algebraický nástroj na simultánne modelovanie pravdivosti a informácie. Boli zavedené N. Belnapom v r. 1977 v článku nazvanom Ako by mal počítač myslieť. Okrem klasických pravdivostných hodnôt t (pravda) a f (nepravda) mal Belnapov príklad aj pravdivostné hodnoty ⅂ (priveľa informácií resp. rozporuplné informácie) a ⅃ (žiadna informácia). Majú aplikácie v umelej inteligencii, logickom programovaní alebo v rozpoznávaní obrazcov. V predchádzajúcej práci týchto autorov z r. 2021 publikovanej v Algebre Universalis sme zaviedli pre každé prirodzené číslo 𝑛 novú triedu bizväzov J𝑛, ktorá zahŕňa Belnapov seminálny príklad (ako bizväz J0). Skonštruovali sme tiež prirodzenú dualitu pre ekvacionálnu triedu V𝑛 algebier generovanú bizväzom J𝑛, kde duálna kategória X𝑛 pozostáva z tzv. multi-sortových topologických štruktúr. V súčasnej nadväzujúcej práci axiomatizujeme duálnu kategóriu X𝑛 a ukazujeme, že je izomorfná s kategóriou Y𝑛 jedno-sortových topologických štruktúr. Ukazujeme ako konštruovať Priestleyovej duál bizväzu v triede V𝑛 prostredníctvom duálu v triede Y𝑛. Ako aplikáciu ukazujeme, že jedno-generovaný voľný bizväz v triede V𝑛 má veľkosť danú konkrétnym polynómom stupňa 6. URL Link na plný text Public work category ADM No. of Archival Copy 52020 Catal.org. BB301 - Univerzitná knižnica Univerzity Mateja Bela v Banskej Bystrici Database xpca - PUBLIKAČNÁ ČINNOSŤ References PERIODIKÁ-Súborný záznam periodika article
Title Expanding Belnap: dualities for a new class of default bilattices Author info Andrew P. K. Craig, Brian A. Davey, Miroslav Haviar Author Craig Andrew, P. K. (34%)
Co-authors Davey Brian A. (33%)
Haviar Miroslav 1965- (33%) UMBFP10 - Katedra matematiky
Source document Algebra universalis. Vol. 81, no. 4 (2020), pp. 1-26. - Basel : Springer Nature Switzerland AG, 2020 Keywords natural duality výsledky - results algebras Form. Descr. články - journal articles Language English Country Switzerland Annotation Bilattices provide an algebraic tool with which to model simultaneously knowledge and truth. They were introduced by Belnap in 1977 in a paper entitled How a computer should think. Belnap argued that instead of using a logic with two values, for ‘true’ and ‘false’, a computer should use a logic with two further values, for ‘contradiction’ and ‘no information´. The resulting structure is equipped with two lattice orders, a knowledge order and a truth order, and hence is called a bilattice. Prioritised default bilattices include not only values for ‘true’, ‘false’, ‘contradiction’ and ‘no information’, but also indexed families of default values for simultaneous modelling of degrees of knowledge and truth. We focus on a new family of prioritised default bilattices: Jn, for all natural numbers n. The bilattice J0 is precisely Belnap’s seminal example. We obtain a multisorted duality for the variety generated by Jn, and separately a single sorted duality for the quasivariety generated by Jn. The main tool for both dualities is a unified approach that enables us to identify the meet-irreducible elements of the appropriate subuniverse lattices. Our results provide an interesting example where the multi-sorted duality for the variety has a simpler structure than the single-sorted duality for the quasivariety URL Link na zdrojový dokument Public work category ADC No. of Archival Copy 48507 Catal.org. BB301 - Univerzitná knižnica Univerzity Mateja Bela v Banskej Bystrici Database xpca - PUBLIKAČNÁ ČINNOSŤ References PERIODIKÁ-Súborný záznam periodika 
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Title Bohr compactifications of algebras and structures Author info B. A. Davey, M. Haviar, H. A. Priestley Author Davey Brian A. (34%)
Co-authors Haviar Miroslav 1965- (33%) UMBFP10 - Katedra matematiky
Priestley Hilary A. (33%)
Source document Applied Categorical Structures. Vol. 25, no. 3 (2017), pp. 403-430. - Dordrecht : Springer, 2017 Person keywords Bohr Niels dánsky fyzik 1885-1962 Keywords natural duality natural extension distributive lattices Stone-Čechova kompaktifikácia - Stone-Čech compactification Language English Country Netherlands systematics 51 Annotation This paper provides a unifying framework for a range of categorical constructions characterised by universal mapping properties, within the realm of compactifications of discrete structures. Some classic examples fit within this broad picture: the Bohr compactification of an abelian group via Pontryagin duality, the zero-dimensional Bohr compactification of a semilattice, and the Nachbin order-compactification of an ordered set. The notion of a natural extension functor is extended to suitable categories of structures and such a functor is shown to yield a reflection into an associated category of topological structures. Our principal results address reconciliation of the natural extension with the Bohr compactification or its zero-dimensional variant. In certain cases the natural extension functor and a Bohr compactification functor are the same; in others the functors have different codomains but may agree on all objects. Coincidence in the stronger sense occurs in the zero-dimensional setting precisely when the domain is a category of structures whose associated topological prevariety is standard. It occurs, in the weaker sense only, for the class of ordered sets and, as we show, also for infinitely many classes of ordered structures. Coincidence results aid understanding of Bohr-type compactifications, which are defined abstractly. Ideas from natural duality theory lead to an explicit description of the natural extension which is particularly amenable for any prevariety of algebras with a finite, dualisable, generator. Examples of such classes-often varieties-are plentiful and varied, and in many cases the associated topological prevariety is standard. Public work category ADM No. of Archival Copy 39736 Database xpca - PUBLIKAČNÁ ČINNOSŤ References PERIODIKÁ-Súborný záznam periodika unrecognised
Title Piggyback dualities revisited Author info Davey B. A., Haviar M., Priestley H. A. Author Davey Brian A. (34%)
Co-authors Haviar Miroslav 1965- (33%) UMBFP10 - Katedra matematiky
Priestley Hilary A. (33%)
Source document Algebra Universalis. Vol. 76, no. 2 (2016), pp. 245-285. - Cham : Springer Nature Switzerland AG, 2016 Keywords duality duality theory Priestley duality Priestleyovská dualita Language English Country Switzerland systematics 51 Public work category ADC No. of Archival Copy 37066 Repercussion category CABRER, Leonardo M. - SPADA, Luca. MV-algebras, infinite dimensional polyhedra, and natural dualities. In Archive for mathematical logic. ISSN 0933-5846, 2017, vol. 56, no. 1-2, pp. 21-42.
Catal.org. BB301 - Univerzitná knižnica Univerzity Mateja Bela v Banskej Bystrici Database xpca - PUBLIKAČNÁ ČINNOSŤ References PERIODIKÁ-Súborný záznam periodika article
Title Davey, Brian A.; Nguyen, Long T.; Pitkethly, Jane G.: Counting relations on Ockham algebras Author info Miroslav Haviar Author Haviar Miroslav 1965- (100%) UMBFP10 - Katedra matematiky
Source document MathSciNet : Mathematical Reviews on the web. online, MR3374657, pp. [1-3]. - Providence : American Mathematical Society, 2015 Review document Counting relations on Ockham algebras / Brian A. Davey, Long T. Nguyen, Jane G. Pitkethly. - Cham : Springer International Publishing, 2015 Keywords matematika - mathematics algebra - algebra recenzie - reviews Language English Country United States of America systematics 51 Public work category EDI No. of Archival Copy 43185 Catal.org. BB301 - Univerzitná knižnica Univerzity Mateja Bela v Banskej Bystrici Database xpca - PUBLIKAČNÁ ČINNOSŤ article
Title Natural dualities in partnership Author info Brian A. Davey, Miroslav Haviar, Hilary A. Priestley Author Davey Brian A. (34%)
Co-authors Haviar Miroslav 1965- (33%) UMBFP10 - Katedra matematiky
Priestley Hilary A. (33%)
Source document Applied Categorical Structures. Vol. 20, no. 6 (2012), pp. 583-602. - Dordrecht : Springer, 2012 Keywords prirodzená dualita prirodzené rozšírenie kanonické rozšírenia natural duality natural extension canonical extension Language English Country Netherlands systematics 512 Public work category ADE No. of Archival Copy 23307 Catal.org. BB301 - Univerzitná knižnica Univerzity Mateja Bela v Banskej Bystrici Database xpca - PUBLIKAČNÁ ČINNOSŤ References PERIODIKÁ-Súborný záznam periodika article
Title Full dualisability is independent of the generating algebra Author info Brian A. Davey, Miroslav Haviar, Jane G. Pitkethly Author Davey Brian A. (34%)
Co-authors Haviar Miroslav 1965- (33%) UMBFP10 - Katedra matematiky
Pitkethly Jane G. (33%)
Source document Algebra Universalis. Vol. 67, no. 3 (2012), pp. 257-272. - Cham : Springer Nature Switzerland AG, 2012 Keywords algebra - algebra teória dualít generujúca algebra duality theory full duality generating algebra Language English Country Switzerland systematics 512 Public work category ADE No. of Archival Copy 22386 Catal.org. BB301 - Univerzitná knižnica Univerzity Mateja Bela v Banskej Bystrici Database xpca - PUBLIKAČNÁ ČINNOSŤ References PERIODIKÁ-Súborný záznam periodika article