EMSO(FO$^2$) 01 law fails for all dense random graphs
Abstract
In this paper, we disprove EMSO(FO$^2$) convergence law for the binomial random graph $G(n,p)$ for any constant probability $p$. More specifically, we prove that there exists an existential monadic second order sentence with 2 first order variables such that, for every $p\in(0,1)$, the probability that it is true on $G(n,p)$ does not converge.
 Publication:

arXiv eprints
 Pub Date:
 June 2021
 DOI:
 10.48550/arXiv.2106.13968
 arXiv:
 arXiv:2106.13968
 Bibcode:
 2021arXiv210613968A
 Keywords:

 Mathematics  Combinatorics