Skip to main content
×
Home
    • Aa
    • Aa
  • Get access
    Check if you have access via personal or institutional login
  • Cited by 4
  • Cited by
    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.

    Jackson, Marcel and Trotta, Belinda 2013. Constraint Satisfaction, Irredundant Axiomatisability and Continuous Colouring. Studia Logica, Vol. 101, Issue. 1, p. 65.


    DOLINKA, IGOR 2012. ON FREE SPECTRA OF A CLASS OF FINITE INVERSE MONOIDS. Journal of the Australian Mathematical Society, Vol. 93, Issue. 03, p. 225.


    Jackson, Marcel and McNulty, George F. 2011. The equational complexity of Lyndon’s algebra. Algebra universalis, Vol. 65, Issue. 3, p. 243.


    Jackson, Marcel and Trotta, Belinda 2010. The Division Relation: Congruence Conditions and Axiomatisability. Communications in Algebra, Vol. 38, Issue. 2, p. 534.


    ×

Flat algebras and the translation of universal Horn logic to equational logic

  • Marcel Jackson (a1)
  • DOI: http://dx.doi.org/10.2178/jsl/1208358744
  • Published online: 01 March 2014
Abstract
Abstract

We describe which subdirectly irreducible flat algebras arise in the variety generated by an arbitrary class of flat algebras with absorbing bottom element. This is used to give an elementary translation of the universal Horn logic of algebras, partial algebras, and more generally still, partial structures into the equational logic of conventional algebras. A number of examples and corollaries follow. For example, the problem of deciding which finite algebras of some fixed type have a finite basis for their quasi-identities is shown to be equivalent to the finite identity basis problem for the finite members of a finiteiy based variety with definable principal congruences.

Copyright
Linked references
Hide All

This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

[1]M. Adams , K. Adaricheva , W. Dziobiak , and A. Kravchenko , Open questions related to the problem of Birkhoff and Maltsev, Studia Logica, vol. 78 (2004), pp. 357378.

[2]M. Adams and W. Dziobiak , The lattice of quasivarieties of undirected graphs, Algebra Universalis, vol. 47 (2002), pp. 711.

[4]K. Baker , G. McNulty , and J. Wang , An extension of Willard's finite basis theorem: Congruence meet-semidistributive varieties of finite critical depth, Algebra Universalis, vol. 52 (2004), pp. 289302.

[5]K. Baker and J. Wang , Definable principal subcongruences, Algebra Universalis, vol. 47 (2002), pp. 145151.

[6]C. Bergman and G. Slutzki , Complexity of some problems concerning varieties and quasi-varieties of algebras, SIAM Journal on Computing, vol. 30 (2000), pp. 359382.

[8]G. Bezhanishvili , Locally finite varieties, Algebra Universalis, vol. 46 (2001), pp. 531548.

[9]P. Burmeister , Partial algebras — survey of a unifying approach towards a two-valued model theory for partial algebras, Algebra Universalis, vol. 15 (1982), pp. 306358.

[12]D. M. Clark , B. A. Davey , R. S. Freese , and M. Jackson , Standard topological algebras: Syntactic and principal congruences and profiniteness, Algebra Universalis, vol. 52 (2004), pp. 343376.

[13]A. H. Clifford and G. B. Preston , The Algebraic Theory of Semigroups, Volume 2, American Mathematical Society, Providence, RI, 1967.

[14]D. Delić , Finite bases for flat graph algebras, Journal of Algebra, vol. 246 (2001), pp. 453469.

[16]S. Eilenberg and M. P. Schützenberger , On pseudovarieties, Advances in Mathematics, vol. 19 (1976), pp. 413418.

[19]M. Jackson , Finiteness properties of varieties and the restriction to finite algebras, Semigroup Forum, vol. 70 (2005), pp. 159187.

[20]M. Jackson and R. McKenzie , Interpreting graph colourability in finite semigroups, International Journal of Algebra and Computation, vol. 16 (2006), pp. 119140.

[21]M. Jackson and T. Stokes , Agreeable semigroups, Journal of Algebra, vol. 266 (2003), pp. 393417.

[22]M. Jackson and T. Stokes , Identities in the algebra of partial maps, International Journal of Algebra and Computation, vol. 16 (2006), pp. 11311159.

[24]J. Ježek , M. Maróti , and R. McKenzie , Quasiequational theories of flat algebras, Czechoslovak Mathematical Journal, vol. 55 (2005), pp. 665675.

[25]J. Kad'ourek , On bases of identities of finite inverse semigroups with solvable subgroups, Semigroup Forum, vol. 67 (2003), pp. 317343.

[26]O. G. Kharlampovich and M. V. Sapir , Algorithmic problems in varieties, International Journal of Algebra and Computation, vol. 5 (1995), pp. 379602.

[28]W. A. Lampe , G. F. McNulty , and R. Willard , Full duality among graph algebras andflat graph algebras, Algebra Universalis, vol. 45 (2001), pp. 311334.

[29]J. Lawrence and R. Willard , On finitely based groups and nonfinitely based quasivarieties, Journal of Algebra, vol. 203 (1998), pp. 111.

[32]R. McKenzie , The residual bounds of finite algebras, International Journal of Algebra and Computation, vol. 6 (1996), no. 1, pp. 128.

[34]R. McKenzie , Tarski's finite basis problem is undecidable, International Journal of Algebra and Computation, vol. 6 (1996), pp. 49104.

[36]J. Nešetřil and A. Pultr , On classes of relations and graphs determined by subobjects and factor objects, Discrete Mathematics, vol. 22 (1978), pp. 287300.

[37]S. Oates and M. B. Powell , Identical relations in finite groups, Journal of Algebra, vol. 1 (1964), pp. 1139.

[39]M.V. Sapir , The lattice of quasivarieties of semigroups, Algebra Universalis, vol. 21 (1985), pp. 172180.

[41]M.V. Sapir , Identities of finite inverse semigroups, International Journal of Algebra and Computation, vol. 3 (1993), pp. 115124.

[43]Z. Szekely , Computational complexity of the finite membership problem forvarieties, International Journal of Algebra and Computation, vol. 12 (2002), pp. 811823.

[45]R. Willard , On McKenzie's method, Periodica Mathematica Hungarica., vol. 32 (1996), pp. 149165.

Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

The Journal of Symbolic Logic
  • ISSN: 0022-4812
  • EISSN: 1943-5886
  • URL: /core/journals/journal-of-symbolic-logic
Please enter your name
Please enter a valid email address
Who would you like to send this to? *
×

Keywords: