The geometry of 1-based minimal types

Tristram De Piro, Byunghan Kim

Research output: Contribution to journalArticlepeer-review

12 Citations (Scopus)


In this paper, we study the geometry of a (nontrivial) 1-based SU rank-1 complete type. We show that if the (localized, resp.) geometry of the type is modular, then the (localized, resp.) geometry is projective over a division ring. However, unlike the stable case, we construct a locally modular type that is not affine. For the general 1-based case, we prove that even if the geometry of the type itself is not projective over a division ring, it is when we consider a 2-fold or 3-fold of the geometry altogether. In particular, it follows that in any ω-categorical, nontrivial, 1-based theory, a vector space over a finite field is interpretable.

Original languageEnglish
Pages (from-to)4241-4263
Number of pages23
JournalTransactions of the American Mathematical Society
Issue number10
Publication statusPublished - 2003 Oct

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics


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