6 found
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  1.  8
    Perfect Trees and Elementary Embeddings.Sy-David Friedman & Katherine Thompson - 2008 - Journal of Symbolic Logic 73 (3):906-918.
    An important technique in large cardinal set theory is that of extending an elementary embedding j: M → N between inner models to an elementary embedding j*: M[G] → N[G*] between generic extensions of them. This technique is crucial both in the study of large cardinal preservation and of internal consistency. In easy cases, such as when forcing to make the GCH hold while preserving a measurable cardinal (via a reverse Easton iteration of α-Cohen forcing for successor cardinals α), the (...)
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  2.  9
    Universality for Orders and Graphs Which Omit Large Substructures.Katherine Thompson - 2006 - Notre Dame Journal of Formal Logic 47 (2):233-248.
    This paper will examine universality spectra for relational theories which cannot be described in first-order logic. We will give a method using functors to show that two types of structures have the same universality spectrum. A combination of methods will be used to show universality results for certain ordered structures and graphs. In some cases, a universal spectrum under GCH will be obtained. Since the theories are not first-order, the classic model theory result under GCH does not hold.
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  3.  9
    An Inner Model for Global Domination.Sy-David Friedman & Katherine Thompson - 2009 - Journal of Symbolic Logic 74 (1):251-264.
    In this paper it is shown that the global statement that the dominating number for k is less than $2^k $ for all regular k, is internally consistent, given the existence of $0^\# $ . The possible range of values for the dominating number for k and $2^k $ which may be simultaneously true in an inner model is also explored.
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  4.  16
    Cogwheels of the Mind: The Story of Venn Diagrams.Katherine Thompson - 2005 - Bulletin of Symbolic Logic 11 (1):83-84.
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  5.  7
    Small Universal Families for Graphs Omitting Cliques Without GCH.Katherine Thompson - 2010 - Archive for Mathematical Logic 49 (7-8):799-811.
    When no single universal model for a set of structures exists at a given cardinal, then one may ask in which models of set theory does there exist a small family which embeds the rest. We show that for λ+-graphs (λ regular) omitting cliques of some finite or uncountable cardinality, it is consistent that there are small universal families and 2λ > λ+. In particular, we get such a result for triangle-free graphs.
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  6.  4
    Internal Consistency for Embedding Complexity.Sy-David Friedman & Katherine Thompson - 2008 - Journal of Symbolic Logic 73 (3):831-844.
    In a previous paper with M. Džamonja, class forcings were given which fixed the complexity (a universality covering number) for certain types of structures of size λ together with the value of 2λ for every regular λ. As part of a programme for examining when such global results can be true in an inner model, we build generics for these class forcings.
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