A dichotomy in classifying quantifiers for finite models

Saharon Shelah*, Mor Doron

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

We consider a family U of finite universes. The second order existential quantifier Q, means for each U ∈ U quantifying over a set of n(ℜ)-place relations isomorphic to a given relation. We define a natural partial order on such quantifiers called interpretability. We show that for every Q, either Qℜ is interpretable by quantifying over subsets of U and one to one functions on U both of bounded order, or the logic L(Q) (first order logic plus the quantifier Q) is undecidable.

Original languageEnglish
Pages (from-to)1297-1324
Number of pages28
JournalJournal of Symbolic Logic
Volume70
Issue number4
DOIs
StatePublished - Dec 2005

Fingerprint

Dive into the research topics of 'A dichotomy in classifying quantifiers for finite models'. Together they form a unique fingerprint.

Cite this