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Archive for Mathematical Logic

, Volume 42, Issue 7, pp 649–663 | Cite as

On the fine structure of the polygroup blow-up

  • Itay Ben-Yaacov
Article

Abstract.

We study in detail the blow-up procedure described in [BTW01]. We obtain a structure theorem for coreless polygroups as a double quotient space G//H, and a polygroup chunk theorem. Seeking to remove the arbitrary parameter needed for the blow-up, we find canonical Ø-invariant groupoids 𝔊 ≤ ℋ analogous to G and H above, and show that ℋ contains precisely all the arbitrary choices related to the blow-up.

Keywords

Simple theories Group configuration Polygroups 

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References

  1. 1.
    Ben-Yaacov, I., Tomašić, I., Wagner, F.O.: Constructing an almost-hyperdefinable group. Preprint, 2001Google Scholar
  2. 2.
    Comer, S.D.: Polygroups derived from cogroups. J. Algebra 89, 397–405 (1984)MathSciNetzbMATHGoogle Scholar
  3. 3.
    Tomašić, I.: Geometric simplicity theory. Ph.D. thesis, University of Edinburgh, 2001Google Scholar
  4. 4.
    Wagner, F.O.: Simple theories. Kluwer Academic Publishers, 2000Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Itay Ben-Yaacov
    • 1
  1. 1.Équipe de Logique MathématiqueUFR de Mathématiques (case 7012), Université ParisFrance

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