# Sh:567

• Baldwin, J. T., & Shelah, S. (1998). DOP and FCP in generic structures. J. Symbolic Logic, 63(2), 427–438.
• Abstract:
Spencer and Shelah [ShSp:304] constructed for each irrational \alpha between 0 and 1 the theory T^\alpha as the almost sure theory of random graphs with edge probability n^{-\alpha}. In [BlSh:528] we proved that this was the same theory as the theory T_\alpha built by constructing a generic model in Baldwin and Shi. In this paper we explore some of the more subtle model theoretic properties of this theory. We show that T^\alpha has the dimensional order property and does not have the finite cover property.
• Version 2003-07-15_10 (18p) published version (13p)
Bib entry
@article{Sh:567,
author = {Baldwin, John T. and Shelah, Saharon},
title = {{DOP and FCP in generic structures}},
journal = {J. Symbolic Logic},
fjournal = {The Journal of Symbolic Logic},
volume = {63},
number = {2},
year = {1998},
pages = {427--438},
issn = {0022-4812},
mrnumber = {1625876},
mrclass = {03C45 (03C13)},
doi = {10.2307/2586841},
note = {\href{https://arxiv.org/abs/math/9607228}{arXiv: math/9607228}},
arxiv_number = {math/9607228},
keyword = {0-1 laws}
}