# Sh:801

- Doron, M., & Shelah, S. (2005).
*A dichotomy in classifying quantifiers for finite models*. J. Symbolic Logic,**70**(4), 1297–1324. arXiv: math/0405091 DOI: 10.2178/jsl/1129642126 MR: 2194248 -
Abstract:

We consider a family \mathfrak{U} of finite universes. The second order quantifier Q_{\mathfrak{R}}, means for each U\in {\mathfrak{U}} quantifying over a set of n({\mathfrak{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_{\mathfrak {R}}, ever Q_{\mathfrak {R}} is interpretable by quantifying over subsets of U and one to one functions on U both of bounded order, or the logic L(Q_{\mathfrak{R}}) (first order logic plus the quantifier Q_{\mathfrak{R}}) is undecidable. - published version (29p)

Bib entry

@article{Sh:801, author = {Doron, Mor and Shelah, Saharon}, title = {{A dichotomy in classifying quantifiers for finite models}}, journal = {J. Symbolic Logic}, fjournal = {The Journal of Symbolic Logic}, volume = {70}, number = {4}, year = {2005}, pages = {1297--1324}, issn = {0022-4812}, doi = {10.2178/jsl/1129642126}, mrclass = {03C85 (03C13)}, mrnumber = {2194248}, mrreviewer = {John T. Baldwin}, doi = {10.2178/jsl/1129642126}, note = {\href{https://arxiv.org/abs/math/0405091}{arXiv: math/0405091}}, arxiv_number = {math/0405091} }