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Bulletin of the Iranian Mathematical Society

, Volume 45, Issue 6, pp 1839–1854 | Cite as

Strict Superstablity and Decidability of Certain Generic Graphs

  • Ali N. Valizadeh
  • Massoud PourmahdianEmail author
Original Paper
  • 10 Downloads

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.

Keywords

Hrushovski constructions Generic structures Strictly superstable Lascar rank Predimension Pseudofinite structures Ultraflat graphs 

Mathematics Subject Classification

03C99 05C63 

Notes

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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Copyright information

© Iranian Mathematical Society 2019

Authors and Affiliations

  1. 1.Department of Mathematics and Computer ScienceAmirkabir University of TechnologyTehranIran
  2. 2.School of MathematicsInstitute for Research in Fundamental Sciences (IPM)TehranIran

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