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ON LATTICES AND THEIR IDEAL LATTICES, AND POSETS AND THEIR IDEAL POSETS
, 2008
"... For P a poset or lattice, let Id(P) denote the poset, respectively, lattice, of upward directed downsets in P, including the empty set, and let id(P) = Id(P) − {∅}. This note obtains various results to the effect that Id(P) is always, and id(P) often, “essentially larger ” than P. In the first v ..."
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(P) is known to be isomorphic to P if and only if P has ascending chain condition. This result is strengthened to say that the only posets P0 such that for every natural number n there exists a poset Pn with id n (Pn) ∼ = P0 are those having ascending chain condition. On the other hand, a wide class of cases
Domain Theory
 Handbook of Logic in Computer Science
, 1994
"... Least fixpoints as meanings of recursive definitions. ..."
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Cited by 546 (25 self)
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Least fixpoints as meanings of recursive definitions.
ON SCATTERED POSETS WITH FINITE DIMENSION
, 812
"... Abstract. We discuss a possible characterization, by means of forbidden configurations, of posets which are embeddable in a product of finitely many scattered chains. Introduction and presentation of the results A fundamental result, due to Szpilrajn [26], states that every order on a set is the int ..."
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Abstract. We discuss a possible characterization, by means of forbidden configurations, of posets which are embeddable in a product of finitely many scattered chains. Introduction and presentation of the results A fundamental result, due to Szpilrajn [26], states that every order on a set
Quasicontinuous posets
 Houston Journal of Mathematics
, 1983
"... The study of the spectral theory of primally generated (and hence distributive) continuous lattices and the resulting duality theory between primally generated continuous lattices and locally quasicompact sober spaces was initiated by K. H. Hofmann and J. D. Lawson in [ 1]. Patterning their work on ..."
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Cited by 9 (0 self)
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finitely many zero coordinates together with 0. Then Spec M and Spec N are both countable antichains the elements having only one zero coordinate. However, since every subset of Spec M uniquely defines an element of M but every infinite subset of
Posets, homomorphisms and homogeneity Abstract
"... Jarik Neˇsetˇril suggested to the first author the investigation of notions of homogeneity for relational structures, where “isomorphism ” is replaced by “homomorphism” in the definition. Here we look in detail at what happens for posets. For the strict order, all five generalisations of homogeneity ..."
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of homogeneity coincide, and we give a characterisation of the countable structures that arise. For the nonstrict order, there is an additional class. The “generic poset ” plays an important role in the investigation. Key words: Poset, homomorphism, homogeneous, relational structure 1
On minimal prime graphs and posets
, 2008
"... We show that there are four infinite prime graphs such that every infinite prime graph with no infinite clique embeds one of these graphs. We derive a similar result for infinite prime posets with no infinite chain or no infinite antichain. ..."
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Cited by 2 (0 self)
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We show that there are four infinite prime graphs such that every infinite prime graph with no infinite clique embeds one of these graphs. We derive a similar result for infinite prime posets with no infinite chain or no infinite antichain.
POSET LIMITS AND EXCHANGEABLE RANDOM POSETS
, 2009
"... We develop a theory of limits of finite posets in close analogy to the recent theory of graph limits. In particular, we study representations of the limits by functions of two variables on a probability space, and connections to exchangeable random infinite posets. ..."
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We develop a theory of limits of finite posets in close analogy to the recent theory of graph limits. In particular, we study representations of the limits by functions of two variables on a probability space, and connections to exchangeable random infinite posets.
Results 1  10
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4,237