Sh:1077

• Shelah, S. Random graph: stronger logic but with the zero one law. Preprint. arXiv: 1511.05383
• Abstract:
  We find a logic really stronger than first order for the random graph with edge probability \frac 12 but satisfies the 0-1 law. This means that on the one hand it satisfies the 0-1 law, e.g. for the random graph {\mathcal G}_{n,1/2} and on the other hand there is a formula \varphi(x) such that for no first order \psi(x) do we have: for every random enough {\mathcal G}_{n,1/2} the formulas \varphi(x),\psi(x) equivalent in it.
• Version 2021-07-15 (20p)

@article{Sh:1077,
 author = {Shelah, Saharon},
 title = {{Random graph: stronger logic but with the zero one law}},
 note = {\href{https://arxiv.org/abs/1511.05383}{arXiv: 1511.05383}},
 arxiv_number = {1511.05383}
}