Potential isomorphism and semi-proper trees

Tom 175 / 2002

Alex Hellsten, Tapani Hyttinen, Saharon Shelah Fundamenta Mathematicae 175 (2002), 127-142 MSC: 03E05, 03C55. DOI: 10.4064/fm175-2-3

Streszczenie

We study a notion of potential isomorphism, where two structures are said to be potentially isomorphic if they are isomorphic in some generic extension that preserves stationary sets and does not add new sets of cardinality less than the cardinality of the models. We introduce the notion of weakly semi-proper trees, and note that there is a strong connection between the existence of potentially isomorphic models for a given complete theory and the existence of weakly semi-proper trees.

We show that the existence of weakly semi-proper trees is consistent relative to ${\rm ZFC}$ by proving the existence of weakly semi-proper trees under certain cardinal arithmetic assumptions. We also prove the consistency of the non-existence of weakly semi-proper trees assuming the consistency of some large cardinals.

Autorzy

  • Alex HellstenDepartment of Mathematics
    University of Helsinki
    00014 Helsinki, Finland
    e-mail
  • Tapani HyttinenDepartment of Mathematics
    University of Helsinki
    00014 Helsinki, Finland
    e-mail
  • Saharon ShelahInstitute of Mathematics
    The Hebrew University
    91904 Jerusalem, Israel
    and
    Department of Mathematics
    Rutgers University
    New Brunswick, NJ 08903, U.S.A.
    e-mail

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