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
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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] - Version 2008-08-02_11 (42p) 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},
mrnumber = {1969657},
mrclass = {03C13 (60C05 60F20)},
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}
}