Corpus ID: 119308070

First order theory on $G(n, c n^{-1})$

  title={First order theory on \$G(n, c n^\{-1\})\$},
  author={M. Podder},
  journal={arXiv: Probability},
  • M. Podder
  • Published 31 January 2018
  • Mathematics
  • arXiv: Probability
A well-known result of Shelah and Spencer tells us that the almost sure theory for first order language on the random graph sequence $\left\{G(n, cn^{-1})\right\}$ is not complete. This paper proposes and proves what the complete set of completions of the almost sure theory for $\left\{G(n, c n^{-1})\right\}$ should be. The almost sure theory $T$ consists of two sentence groups: the first states that all the components are trees or unicyclic components, and the second states that, given any $k… Expand


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