8 found
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  1.  4
    J. B. Nation (2003). Formal Descriptions of Developing Systems: An Overview. In Formal Descriptions of Developing Systems. Kluwer Academic Publishers 1--7.
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  2.  12
    J. B. Nation (2013). Lattices of Theories in Languages Without Equality. Notre Dame Journal of Formal Logic 54 (2):167-175.
    If $\mathbf{S}$ is a semilattice with operators, then there is an implicational theory $\mathscr{Q}$ such that the congruence lattice $\operatorname{Con}$ is isomorphic to the lattice of all implicational theories containing $\mathscr{Q}$.
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  3.  12
    K. Adaricheva, R. Mckenzie, E. R. Zenk, M. Mar´ti & J. B. Nation (2006). The Jónsson-Kiefer Property. Studia Logica 83 (1-3):111 - 131.
    The least element 0 of a finite meet semi-distributive lattice is a meet of meet-prime elements. We investigate conditions under which the least element of an algebraic, meet semi-distributive lattice is a (complete) meet of meet-prime elements. For example, this is true if the lattice has only countably many compact elements, or if |L| < 2ℵ0, or if L is in the variety generated by a finite meet semi-distributive lattice. We give an example of an algebraic, meet semi-distributive lattice that (...)
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  4.  3
    J. B. Nation (2013). Lattices of Theories in Languages Without Equality. Notre Dame Journal of Formal Logic 54 (2):167-175.
    If $\mathbf{S}$ is a semilattice with operators, then there is an implicational theory $\mathscr{Q}$ such that the congruence lattice $\operatorname{Con}$ is isomorphic to the lattice of all implicational theories containing $\mathscr{Q}$.
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  5.  1
    Ralph Freese, George F. McNulty & J. B. Nation (2002). Inherently Nonfinitely Based Lattices. Annals of Pure and Applied Logic 115 (1-3):175-193.
    We give a general method for constructing lattices L whose equational theories are inherently nonfinitely based. This means that the equational class generated by L is locally finite and that L belongs to no locally finite finitely axiomatizable equational class. We also provide an example of a lattice which fails to be inherently nonfinitely based but whose equational theory is not finitely axiomatizable.
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  6. K. Adaricheva, R. Mckenzie, E. R. Zenk, M. Mar´ti & J. B. Nation (2006). The Jónsson-Kiefer Property. Studia Logica 83 (1-3):111-131.
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  7. Jennifer Hyndman, J. B. Nation & Joy Nishida (forthcoming). Congruence Lattices of Semilattices with Operators. Studia Logica:1-12.
    The duality between congruence lattices of semilattices, and algebraic subsets of an algebraic lattice, is extended to include semilattices with operators. For a set G of operators on a semilattice S, we have \ \cong^{d} {{\rm S}_{p}}}\), where L is the ideal lattice of S, and H is a corresponding set of adjoint maps on L. This duality is used to find some representations of lattices as congruence lattices of semilattices with operators. It is also shown that these congruence lattices (...)
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  8.  5
    J. B. Nation (ed.) (2003). Formal Descriptions of Developing Systems. Kluwer Academic Publishers.
    A cutting-edge survey of formal methods directed specifically at dealing with the deep mathematical problems engendered by the study of developing systems, in particular dealing with developing phase spaces, changing components, structures and functionalities, and the problem of emergence. Several papers deal with the modelling of particular experimental situations in population biology, economics and plant and muscle developments in addition to purely theoretical approaches. Novel approaches include differential inclusions and viability theory, growth tensors, archetypal dynamics, ensembles with variable structures, and (...)
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