Switch to: References

Add citations

You must login to add citations.
  1. Unidimensional modules: uniqueness of maximal non-modular submodels.Anand Pillay & Philipp Rothmaler - 1993 - Annals of Pure and Applied Logic 62 (2):175-181.
    We characterize the non-modular models of a unidimensional first-order theory of modules as the elementary submodels of its prime pure-injective model. We show that in case the maximal non-modular submodel of a given model splits off this is true for every such submodel, and we thus obtain a cancellation result for this situation. Although the theories in question always have models whose maximal non-modular submodel do split off, they may as well have others where they don't. We present a corresponding (...)
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark  
  • Tiny models of categorical theories.M. C. Laskowski, A. Pillay & P. Rothmaler - 1992 - Archive for Mathematical Logic 31 (6):385-396.
    We explore the existence and the size of infinite models of categorical theories having cardinality less than the size of the associated Tarski-Lindenbaum algebra. Restricting to totally transcendental, categorical theories we show that “Every tiny model is countable” is independent of ZFC. IfT is trivial there is at most one tiny model, which must be the algebraic closure of the empty set. We give a new proof that there are no tiny models ifT is not totally transcendental and is non-trivial.
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  • On the number of models of uncountable theories.Ambar Chowdhury & Anand Pillay - 1994 - Journal of Symbolic Logic 59 (4):1285-1300.
    In this paper we establish the following theorems. THEOREM A. Let T be a complete first-order theory which is uncountable. Then: (i) I(|T|, T) ≥ ℵ 0 . (ii) If T is not unidimensional, then for any λ ≥ |T|, I (λ, T) ≥ ℵ 0 . THEOREM B. Let T be superstable, not totally transcendental and nonmultidimensional. Let θ(x) be a formula of least R ∞ rank which does not have Morley rank, and let p be any stationary completion (...)
    Direct download (7 more)  
     
    Export citation  
     
    Bookmark   2 citations  
  • On the number of nonisomorphic models of size |t|.Ambar Chowdhury - 1994 - Journal of Symbolic Logic 59 (1):41 - 59.
    Let T be an uncountable, superstable theory. In this paper we prove Theorem A. If T has finite rank, then I(|T|, T) ≥ ℵ0. Theorem B. If T is trivial, then I(|T|, T) ≥ ℵ0.
    Direct download (8 more)  
     
    Export citation  
     
    Bookmark   2 citations