Random graphs in the monadic theory of order

Shmuel Lifsches; Saharon Shelah

doi:10.1007/s001530050129

Random graphs in the monadic theory of order

Shmuel Lifsches^*
, Saharon Shelah

^*Corresponding author for this work

Einstein Institute of Mathematics

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

Abstract

We continue the works of Gurevich-Shelah and Lifsches-Shelah by showing that it is consistent with ZFC that the first-order theory of random graphs is not interpretable in the monadic theory of all chains. It is provable from ZFC that the theory of random graphs is not interpretable in the monadic second order theory of short chains (hence, in the monadic theory of the real line).

Original language	English
Pages (from-to)	273-312
Number of pages	40
Journal	Archive for Mathematical Logic
Volume	38
Issue number	4-5
DOIs	https://doi.org/10.1007/s001530050129
State	Published - May 1999

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abstract = "We continue the works of Gurevich-Shelah and Lifsches-Shelah by showing that it is consistent with ZFC that the first-order theory of random graphs is not interpretable in the monadic theory of all chains. It is provable from ZFC that the theory of random graphs is not interpretable in the monadic second order theory of short chains (hence, in the monadic theory of the real line).",

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AB - We continue the works of Gurevich-Shelah and Lifsches-Shelah by showing that it is consistent with ZFC that the first-order theory of random graphs is not interpretable in the monadic theory of all chains. It is provable from ZFC that the theory of random graphs is not interpretable in the monadic second order theory of short chains (hence, in the monadic theory of the real line).

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Random graphs in the monadic theory of order

Abstract

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