# Sh:528

- Baldwin, J. T., & Shelah, S. (1997).
*Randomness and semigenericity*. Trans. Amer. Math. Soc.,**349**(4), 1359–1376. arXiv: math/9607226 DOI: 10.1090/S0002-9947-97-01869-2 MR: 1407480 -
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.

- 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}, doi = {10.1090/S0002-9947-97-01869-2}, mrclass = {03C13 (03C50 60B99)}, mrnumber = {1407480}, mrreviewer = {M. Yasuhara}, doi = {10.1090/S0002-9947-97-01869-2}, note = {\href{https://arxiv.org/abs/math/9607226}{arXiv: math/9607226}}, arxiv_number = {math/9607226} }