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

@article{Podder2018FirstOT, title={First order theory on \$G(n, c n^\{-1\})\$}, author={M. Podder}, journal={arXiv: Probability}, year={2018} }

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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