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2 results

  • WOODIN FOR STRONG COMPACTNESS CARDINALS

  • STAMATIS DIMOPOULOS
  • Journal:
    The Journal of Symbolic Logic / Volume 84 / Issue 1 / March 2019
    Published online by Cambridge University Press:
    14 March 2019, pp. 301-319
    Print publication:
    March 2019

  • Woodin and Vopěnka cardinals are established notions in the large cardinal hierarchy and it is known that Vopěnka cardinals are the Woodin analogue for supercompactness. Here we give the definition of Woodin for strong compactness cardinals, the Woodinised version of strong compactness, and we prove an analogue of Magidor’s identity crisis theorem for the first strongly compact cardinal.

  • On Colimits and Elementary Embeddings

  • Joan Bagaria, Andrew Brooke-Taylor
  • Journal:
    The Journal of Symbolic Logic / Volume 78 / Issue 2 / June 2013
    Published online by Cambridge University Press:
    12 March 2014, pp. 562-578
    Print publication:
    June 2013

  • We give a sharper version of a theorem of Rosický, Trnková and Adámek [13], and a new proof of a theorem of Rosický [12], both about colimits in categories of structures. Unlike the original proofs, which use category-theoretic methods, we use set-theoretic arguments involving elementary embeddings given by large cardinals such as α-strongly compact and C(n)-extendible cardinals.