Sh:551
- Shelah, S. (1996). In the random graph , : if has probability for every then it has probability for some . Ann. Pure Appl. Logic, 82(1), 97–102. arXiv: math/9512228 DOI: 10.1016/0168-0072(95)00071-2 MR: 1416640
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Abstract:
Shelah Spencer [ShSp:304] proved the law for the random graphs , , irrational (set of nodes in , the edges are drawn independently, probability of edge is ). One may wonder what can we say on sentences for which Prob converge to zero, Lynch asked the question and did the analysis, getting (for every ):EITHER [] Prob for some such that
OR [] Prob for every .
Lynch conjectured that in case we have
[] Prob for some . We prove it here.
- Version 1995-12-22_10 (8p) published version (6p)
Bib entry
@article{Sh:551, author = {Shelah, Saharon}, title = {{In the random graph $G(n,p)$, $p=n^{-a}$: if $\psi$ has probability $O(n^{-\epsilon})$ for every $\epsilon>0$ then it has probability $O(e^{-n^\epsilon})$ for some $\epsilon>0$}}, journal = {Ann. Pure Appl. Logic}, fjournal = {Annals of Pure and Applied Logic}, volume = {82}, number = {1}, year = {1996}, pages = {97--102}, issn = {0168-0072}, mrnumber = {1416640}, mrclass = {03C13 (05C80 60F20)}, doi = {10.1016/0168-0072(95)00071-2}, note = {\href{https://arxiv.org/abs/math/9512228}{arXiv: math/9512228}}, arxiv_number = {math/9512228} }