Invariant version of cardinality quantifiers in superstable theories

Alexander Berenstein, Ziv Shami

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


We generalize Shelah's analysis of cardinality quantifiers from Chapter V of Classification Theory and the Number of Nonisomorphic Models for a superstable theory. We start with a set of bounds for the cardinality of each formula in some general invariant family of formulas in a superstable theory (in Classification Theory, a uniform family of formulas is considered) and find a set of derived bounds for all formulas. The set of derived bounds is sharp: up to a technical restriction every model that satisfies the original bounds has a sufficiently saturated elementary extension that satisfies the original bounds and such that for each formula the set of its realizations in the extension has arbitrarily large cardinality below the corresponding derived bound of the formula.

Original languageEnglish
Pages (from-to)343-351
Number of pages9
JournalNotre Dame Journal of Formal Logic
Issue number3
StatePublished - 2006
Externally publishedYes


  • Cardinality quantifiers
  • Superstable theories


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