# Sh:467

- Shelah, S. (2002).
*Zero-one laws for graphs with edge probabilities decaying with distance. I*. Fund. Math.,**175**(3), 195–239. arXiv: math/9606226 DOI: 10.4064/fm175-3-1 MR: 1969657 -
Abstract:

Let G_n be the random graph on [n]=\{1,\ldots,n\} with the possible edge \{i,j\} having probability being p_{|i-j|}= 1/|i-j|^\alpha, \alpha\in (0,1) irrational. We prove that the zero one law (for first order logic) holds. The paper is continued in [Sh:517] - published version (45p)

Bib entry

@article{Sh:467, author = {Shelah, Saharon}, title = {{Zero-one laws for graphs with edge probabilities decaying with distance. I}}, journal = {Fund. Math.}, fjournal = {Fundamenta Mathematicae}, volume = {175}, number = {3}, year = {2002}, pages = {195--239}, issn = {0016-2736}, doi = {10.4064/fm175-3-1}, mrclass = {03C13 (60C05 60F20)}, mrnumber = {1969657}, mrreviewer = {Andreas Blass}, doi = {10.4064/fm175-3-1}, note = {\href{https://arxiv.org/abs/math/9606226}{arXiv: math/9606226}}, arxiv_number = {math/9606226}, keyword = {0-1 laws} }