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Infinite spectra in the first order theory of graphs

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Abstract

The psectrum Spec(A) of a sentenceA is, roughly, the set of those a for whichA has a threshold function at or nearp=n −a. Examples are given ofA with infinite spectra and with spectra of order typeΩ i for arbitraryi.

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References

  1. P. Erdös andA. Rényi, On the evolution of random graphs,Publ. Math. Inst. Hung. Acad. Sci.,5 (1960), 17–61.

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  2. S. Shelah andJ. Spencer, Zero-One Laws for Sparse Random Graphs,J. Amer. Math. Soc.,1 (1988), 97–115.

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Authors and Affiliations

  1. Courant Institute, 251 Mercer St., 10012, New York, USA

    J. Spencer

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  1. J. Spencer
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Spencer, J. Infinite spectra in the first order theory of graphs. Combinatorica 10, 95–102 (1990). https://doi.org/10.1007/BF02122699

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  • DOI: https://doi.org/10.1007/BF02122699

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