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Strict Superstablity and Decidability of Certain Generic Graphs

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Abstract

We show that the Hrushovski–Fraïssé limit of certain classes of trees lead to strictly superstable theories of various U-ranks. In fact, for each \( \alpha \in \omega +1\backslash \{0\}\) we introduce a strictly superstable theory of U-rank \( \alpha \). Furthermore, we show that these theories are decidable and pseudofinite.

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Acknowledgements

We would like to thank J. Baldwin, C. Laskowski and D. Macpherson for the helpful discussions we had during our stay at the Institute Henri Poincaré (IHP). Hereby, we also would like to thank IHP and CIMPA for supporting our participation in the trimester MOCOVA 2018 held at the IHP. Also, the authors are thankful to the anonymous referee for his useful suggestions and comments.

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Authors and Affiliations

  1. Department of Mathematics and Computer Science, Amirkabir University of Technology, Tehran, Iran

    Ali N. Valizadeh & Massoud Pourmahdian

  2. School of Mathematics, Institute for Research in Fundamental Sciences (IPM), Tehran, Iran

    Massoud Pourmahdian

Authors
  1. Ali N. Valizadeh
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  2. Massoud Pourmahdian
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Correspondence to Massoud Pourmahdian.

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Communicated by Hamid Reza Ebrahimi Vishki.

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Valizadeh, A.N., Pourmahdian, M. Strict Superstablity and Decidability of Certain Generic Graphs. Bull. Iran. Math. Soc. 45, 1839–1854 (2019). https://doi.org/10.1007/s41980-019-00234-2

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  • DOI: https://doi.org/10.1007/s41980-019-00234-2

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