# Sh:528

• Baldwin, J. T., & Shelah, S. (1997). Randomness and semigenericity. Trans. Amer. Math. Soc., 349(4), 1359–1376.
• Abstract:
Let L contain only the equality symbol and let L^+ be an arbitrary finite symmetric relational language containing L. Suppose probabilities are defined on finite L^+ structures with "edge probability" n^{-\alpha}. By T^\alpha, the almost sure theory of random L^+-structures we mean the collection of L^+-sentences which have limit probability 1. T_\alpha denotes the theory of the generic structures for K_\alpha, (the collection of finite graphs G with \delta_{\alpha}(G)=|G|-\alpha\cdot |\text{edges of $G$}| hereditarily nonnegative.)

THEOREM: T_\alpha, the almost sure theory of random L^+-structures is the same as the theory T_\alpha of the K_\alpha-generic model. This theory is complete, stable, and nearly model complete. Moreover, it has the finite model property and has only infinite models so is not finitely axiomatizable.

• Current version: 1996-07-11_10 (27p) published version (18p)
Bib entry
@article{Sh:528,
author = {Baldwin, John T. and Shelah, Saharon},
title = {{Randomness and semigenericity}},
journal = {Trans. Amer. Math. Soc.},
fjournal = {Transactions of the American Mathematical Society},
volume = {349},
number = {4},
year = {1997},
pages = {1359--1376},
issn = {0002-9947},
mrnumber = {1407480},
mrclass = {03C13 (03C50 60B99)},
doi = {10.1090/S0002-9947-97-01869-2},
note = {\href{https://arxiv.org/abs/math/9607226}{arXiv: math/9607226}},
arxiv_number = {math/9607226}
}