Natural dualities for varieties generated by finite positive MV-chains

POIGER, Wolfgang

doi:10.1007/s00012-024-00868-2

Download

Article (Scientific journals)

Natural dualities for varieties generated by finite positive MV-chains

POIGER, Wolfgang

2024 • In Algebra Universalis, 85

Peer Reviewed verified by ORBi

Permalink
https://hdl.handle.net/10993/61987

DOI
10.1007/s00012-024-00868-2

Files (1)Send to Details Statistics Bibliography Similar publications

Files

Full Text

2309.16998v2.pdf

Author preprint (335.57 kB)

Download

All documents in ORBilu are protected by a user license.

Send to

RIS BibTex APA Chicago Permalink X Linkedin

Details

Keywords :

Positive MV-algebras; Natural dualities; Lukasiewicz logic; Priestley duality; Boolean power

Abstract :

[en] We provide a simple natural duality for the varieties generated by the negation- and implication-free reduct of a finite MV-chain. We study these varieties through the dual equivalences thus obtained. For example, we fully characterize their algebraically closed, existentially closed and injective members. We also explore the relationship between this natural duality and Priestley duality in terms of distributive skeletons and Priestley powers.

Disciplines :

Mathematics

Author, co-author :

POIGER, Wolfgang ; University of Luxembourg > Faculty of Science, Technology and Medicine (FSTM) > Department of Mathematics (DMATH)

External co-authors :

Language :

English

Title :

Natural dualities for varieties generated by finite positive MV-chains

Publication date :

06 September 2024

Journal title :

Algebra Universalis

ISSN :

0002-5240

eISSN :

1420-8911

Publisher :

Birkhauser Verlag, Switzerland

Volume :

Peer reviewed :

Peer Reviewed verified by ORBi

FnR Project :

PRIDE17/12246620/GPS

Funding text :

The author is supported by the Luxembourg National Research Fund under the project PRIDE17/12246620/GPS.

Available on ORBilu :

since 06 September 2024

Statistics

Number of views

93 (2 by Unilu)

Number of downloads

52 (0 by Unilu)

More statistics

Scopus citations^®

Scopus citations^®
without self-citations

OpenCitations

OpenAlex citations

Bibliography

M. Abbadini P. Jipsen T. Kroupa S. Vannucci A finite axiomatization of positive MV-algebras Algebra Univers. 2022 83 1134 1164 4447154 10.1007/s00012-022-00776-3
V. Boicescu A. Filipoiu G. Georgescu S. Rudeanu Łukasiewicz–Moisil Algebras. Annals of Discrete Mathematics 1991 Amsterdam North-Holland
F. Bou F. Esteva L. Godo R.O. Rodríguez On the minimum many-valued modal logic over a finite residuated lattice J. Log. Comput. 2011 21 739 790 2836577 10.1093/logcom/exp062
S. Burris Boolean powers Algebra Univers. 1975 5 341 360 447078 10.1007/BF02485268
S. Burris H.P. Sankappanavar A Course in Universal Algebra. Graduate Texts in Mathematics 1981 New York Springer
C.C. Chang Algebraic analysis of many valued logics Trans. Am. Math. Soc. 1958 88 467 490 94302 10.1090/S0002-9947-1958-0094302-9
R.L.O. Cignoli I.M.L. D’Ottaviano D. Mundici Algebraic Foundations of Many-Valued Reasoning. Trends in Logic 2000 Dordrecht Springer 10.1007/978-94-015-9480-6
R.L.O. Cignoli V. Marra Stone duality for real-valued multisets Forum Math. 2012 24 1317 1331 2996994 10.1515/form.2011.109
D.M. Clark B.A. Davey Natural Dualities for the Working Algebraist. Cambridge Studies in Advanced Mathematics 1998 Cambridge Cambridge University Press
A. Di Nola A. Lettieri One chain generated varieties of MV-algebras J. Algebra 2000 225 667 697 1741557 10.1006/jabr.1999.8136
E.J. Dubuc Y.A. Poveda Representation theory of MV-algebras Ann. Pure Appl. Logic 2010 161 1024 1046 2629504 10.1016/j.apal.2009.12.006
J.M. Dunn Positive modal logic Stud. Log. 1995 55 301 317 1357863 10.1007/BF01061239
A.L. Foster A.F. Pixley Semi-categorical algebras. I. Semi-primal algebras Math. Z. 1964 83 147 169 163866 10.1007/BF01111252
W. Fussner M. Gehrke S.J. van Gool V. Marra Priestley duality for MV-algebras and beyond Forum Math. 2021 33 899 921 4279113 10.1515/forum-2020-0115
M. Gehrke S.J. van Gool V. Marra Sheaf representations of MV-algebras and lattice-ordered abelian groups via duality J. Algebra 2014 417 290 332 3244648 10.1016/j.jalgebra.2014.06.031
R. Grigolia R. Wójcicki G. Malinowski Algebraic Analysis of Łukasiewicz–Tarski’s n-Valued Logical Systems Selected Papers on Łukasiewicz Sentential Calculi 1977 Wrocław Ossolineum 81 92
G. Hansoul B. Teheux Extending Łukasiewicz logics with a modality: algebraic approach to relational semantics Stud. Log. 2013 101 505 545 10.1007/s11225-012-9396-9
A. Iorgulescu Connections between MVn algebras and n-valued Łukasiewicz–Moisil algebras. Part I Discrete Math. 1998 181 155 177 1600763 10.1016/S0012-365X(97)00052-6
P. Jipsen Generalizations of Boolean products for lattice-ordered algebras Ann. Pure Appl. Log. 2009 161 228 234 2552742 10.1016/j.apal.2009.05.005
B. Jónsson Algebras whose congruence lattices are distributive Math. Scand. 1967 21 110 121 237402 10.7146/math.scand.a-10850
A. Kurz W. Poiger B. Teheux New perspectives on semi-primal varieties J. Pure Appl. Algebra 2024 228 4643790 10.1016/j.jpaa.2023.107525
A. Lenkehegyi A direct definition of distributive extensions of partially ordered algebras Acta Math. Hungar. 1986 47 157 160 836407 10.1007/BF01949137
N.G. Martínez H.A. Priestley On Priestley spaces of lattice-ordered algebraic structures Order 1998 15 297 323 1741105 10.1023/A:1006224930256
D. Mundici Advanced Łukasiewicz Calculus and MV-Algebras. Trends in Logic 2011 Dordrecht Springer 10.1007/978-94-007-0840-2
P. Niederkorn Natural dualities for varieties of MV-algebras, I J. Math. Anal. Appl. 2001 255 58 73 1813809 10.1006/jmaa.2000.7153
P. Ostermann Many-valued modal propositional calculi Math. Log. Q. 1988 34 343 354 950369 10.1002/malq.19880340411
J. Schmid Algebraically and existentially closed distributive lattices Math. Log. Q. 1979 25 525 530 549471 10.1002/malq.19790253304