PL EN


Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
Tytuł artykułu

Canonical extensions and completions of posets and lattices

Wybrane pełne teksty z tego czasopisma
Identyfikatory
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
The purpose of this note is to expose a new way of viewing the canonical extension of posets and bounded lattices. Specifically, we seek to expose categorical features of this completion and to reveal its relationship to other completion processes.
Słowa kluczowe
Rocznik
Tom
Strony
133--152
Opis fizyczny
Bibliogr. 20 poz., rys.
Twórcy
autor
  • IMAPP, Radboud Universiteit, PO Box 9010, 6500 GL Nijmegen, Netherlands Mathematical Institute, University of Oxford, 24/29 St Giles, Oxford OX1 3LB, United Kingdom, M.Gehrke@math.ru.nl
Bibliografia
  • [1] B. Banaschewski and G. Bruns, Categorical characterisation of the MacNeille completion, Arch. Math. XVIII (1967), 369–377.
  • [2] B.A. Davey and H.A. Priestley, Introduction to Lattices and Order 2nd edition (Cambridge University Press, 2002).
  • [3] J.M. Dunn, M. Gehrke and A. Palmigiano, Canonical extensions of ordered algebraic structures and relational completeness of some substructural logics, J. Symb. Logic 70 (2005), pp. 713–740.
  • [4] J.M. Dunn and C. Hartonas, Stone duality for lattices, Algebra Universalis 37 (1997), pp. 391–401.
  • [5] M. Erné, Adjunctions and standard constructions for partially ordered sets Contributions to General Algebra 2 (1983), pp. 77–106.
  • [6] M. Erné, The Dedekind–MacNeille completion as a reflector, Order, 8 (1991), pp. 159–173.
  • [7] M. Gehrke, Generalized Kripke frames, Studia Logica, 84 (2006), pp. 241–275.
  • [8] M. Gehrke and J. Harding, Bounded lattice expansions, J. Algebra 238 (2001), pp. 345–371.
  • [9] M. Gehrke and B. Jónsson, Bounded distributive lattices with operators, Math. Japonica 40 (1994), pp. 207–215.
  • [10] M. Gehrke and B. Jónsson, Bounded distributive lattice expansions, Math. Scand. 94 (2004), pp. 13–45.
  • [11] G. Gierz, G., K.H. Hofmann, K. Keimel, J.D. Lawson, M. Mislove and D.S. Scott, Continuous Lattices and Domains, (Cambridge University Press, 2003).
  • [12] S. Ghilardi and G. Meloni, Constructive canonicity in non-classical logics, Ann. Pure Appl. Logic 86 (1997), pp. 1–32.
  • [13] J. Harding, Canonical completions of lattices and ortholattices, Tatra Mountains Math. Publ. 15 (1998), pp. 85–96.
  • [14] G. Hartung, A topological representation of latties, Algebra Universalis 29 (1992), pp. 273–299.
  • [15] B. Jónsson and A. Tarski, Boolean algebras with operators, I, Amer. J. Math. 73 (1951), pp. 891–939.
  • [16] B. Jóonsson and A. Tarski, Boolean algebras with operators, II, Amer. J. Math. 74 (1952), pp. 127–162.
  • [17] G.S. Plotkin, Post-graduate lecture notes in advanced domain theory, incorporating the “Pisa Notes” (Department of Computer Science, University of Edinburgh, 1981; available on-line).
  • [18] J. Schmidt, Zur Kennzeichnung der Dedekind–MacNeilleschen Hulle einer geordneten Menge, Archiv d. Math.7 (1956), pp. 241–249.
  • [19] J. Schmidt, Universal and internal properties of some extensions of partially ordered sets, J. Reine u. Angewandte Math. 253 (1972), pp. 28–42.
  • [20] A. Urquhart, A topological representation theory for lattices, Algebra Universalis 8 (1979), pp. 45–58.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BUJ6-0027-0025
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.