Results for 'Ramifiability'

4 found
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  1.  7
    Large Cardinals and Ramifiability for Directed Sets.R. Hinnion & O. Esser - 2000 - Mathematical Logic Quarterly 46 (1):25-34.
    The notion of “ramifiability” , usually applied to cardinals, can be extended to directed sets and is put in relation here with familiar “large cardinal” properties.
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  2.  16
    On the Consistency of a Positive Theory.Olivier Esser - 1999 - Mathematical Logic Quarterly 45 (1):105-116.
    In positive theories, we have an axiom scheme of comprehension for positive formulas. We study here the “generalized positive” theory GPK∞+. Natural models of this theory are hyperuniverses. The author has shown in [2] that GPK∞+ interprets the Kelley Morse class theory. Here we prove that GPK∞+ + ACWF and the Kelley-Morse class theory with the axiom of global choice and the axiom “On is ramifiable” are mutually interpretable. This shows that GPK∞+ + ACWF is a “strong” theory since “On (...)
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  3.  21
    Tree‐Properties for Ordered Sets.Olivier Esser & Roland Hinnion - 2002 - Mathematical Logic Quarterly 48 (2):213-219.
    In this paper, we study the notion of arborescent ordered sets, a generalizationof the notion of tree-property for cardinals. This notion was already studied previously in the case of directed sets. Our main result gives a geometric condition for an order to be ℵ0-arborescent.
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  4.  4
    Combinatorial Criteria for Ramifiable Ordered Sets.R. Hinnion & O. Esser - 2001 - Mathematical Logic Quarterly 47 (4):539-556.
    The tree-property and its variants make sense also for directed sets and even for partially ordered sets. A combinatoria approach is developed here, with characterizations and criteria involving adequate families of special substructures of directed sets. These substructures form a natural hierarchy that is also investigated.
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