Corpus ID: 119308070

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}
}
  • 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

References

SHOWING 1-5 OF 5 REFERENCES
Zero-one laws for sparse random graphs
For random graph theorists (see, e.g., Bollobas [1] for general reference) p "any constant" is not the only, not even the most interesting case. Rather, they consider p = p(n), a function approachingExpand
Descriptive Complexity
  • N. Immerman
  • Computer Science
  • Graduate Texts in Computer Science
  • 1999
TLDR
The core of the book is contained in Chapters 1 through 7, although even here some sections can be omitted according to the taste and interests of the instructor, and the remaining chapters are more independent of each other. Expand
The Probabilistic Method
TLDR
A particular set of problems - all dealing with “good” colorings of an underlying set of points relative to a given family of sets - is explored. Expand
The Strange Logic of Random Graphs
The study of random graphs was begun in the 1960s and now has a comprehensive literature. This excellent book by one of the top researchers in the field now joins the study of random graphs (andExpand
Die Vollständigkeit der Axiome des logischen Funktionenkalküls
Jakina da Whiteheadek eta Russellek logika eta matematika eraiki dutela ageriko zenbait proposizio axiomatzat hartuz, eta horietatik, zehatz azaldutako inferentzia printzipioetan oinarrituz, logikakoExpand