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  1. More undecidable lattices of Steinitz exchange systems.L. R. Galminas & John W. Rosenthal - 2002 - Journal of Symbolic Logic 67 (2):859-878.
    We show that the first order theory of the lattice $\mathscr{L}^{ (S) of finite dimensional closed subsets of any nontrivial infinite dimensional Steinitz Exhange System S has logical complexity at least that of first order number theory and that the first order theory of the lattice L(S ∞ ) of computably enumerable closed subsets of any nontrivial infinite dimensional computable Steinitz Exchange System S ∞ has logical complexity exactly that of first order number theory. Thus, for example, the lattice of (...)
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  • Elementary equivalence of infinite-dimensional classical groups.Vladimir Tolstykh - 2000 - Annals of Pure and Applied Logic 105 (1-3):103-156.
    Let D be a division ring such that the number of conjugacy classes of the multiplicative group D ∗ is equal to the power of D ∗ . Suppose that H is the group GL or PGL, where V is a vector space of infinite dimension ϰ over D . We prove, in particular, that, uniformly in κ and D , the first-order theory of H is mutually syntactically interpretable with the theory of the two-sorted structure 〈κ,D〉 in the second-order (...)
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