TY - JOUR

T1 - Invariant version of cardinality quantifiers in superstable theories

AU - Berenstein, Alexander

AU - Shami, Ziv

PY - 2006

Y1 - 2006

N2 - 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.

AB - 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.

KW - Cardinality quantifiers

KW - Superstable theories

UR - http://www.scopus.com/inward/record.url?scp=79961097623&partnerID=8YFLogxK

U2 - 10.1305/ndjfl/1163775441

DO - 10.1305/ndjfl/1163775441

M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???

AN - SCOPUS:79961097623

SN - 0029-4527

VL - 47

SP - 343

EP - 351

JO - Notre Dame Journal of Formal Logic

JF - Notre Dame Journal of Formal Logic

IS - 3

ER -