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  1. One-Basedness and Groups of the Form G/G 00.Davide Penazzi - 2011 - Archive for Mathematical Logic 50 (7-8):743-758.
    We initiate a geometric stability study of groups of the form G/G 00, where G is a 1-dimensional definably compact, definably connected, definable group in a real closed field M. We consider an enriched structure M′ with a predicate for G 00 and check 1-basedness or non-1-basedness for G/G 00, where G is an additive truncation of M, a multiplicative truncation of M, SO 2(M) or one of its truncations; such groups G/G 00 are now interpretable in M′. We prove (...)
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  • The Elementary Theory of Dedekind Cuts in Polynomially Bounded Structures.Marcus Tressl - 2005 - Annals of Pure and Applied Logic 135 (1-3):113-134.
    Let M be a polynomially bounded, o-minimal structure with archimedean prime model, for example if M is a real closed field. Let C be a convex and unbounded subset of M. We determine the first order theory of the structure M expanded by the set C. We do this also over any given set of parameters from M, which yields a description of all subsets of Mn, definable in the expanded structure.
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  • Pseudo Completions and Completions in Stages of o-Minimal Structures.Marcus Tressl - 2006 - Archive for Mathematical Logic 45 (8):983-1009.
    For an o-minimal expansion R of a real closed field and a set $\fancyscript{V}$ of Th(R)-convex valuation rings, we construct a “pseudo completion” with respect to $\fancyscript{V}$ . This is an elementary extension S of R generated by all completions of all the residue fields of the $V \in \fancyscript{V}$ , when these completions are embedded into a big elementary extension of R. It is shown that S does not depend on the various embeddings up to an R-isomorphism. For polynomially (...)
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  • Arithmetic of Dedekind Cuts of Ordered Abelian Groups.Antongiulio Fornasiero & Marcello Mamino - 2008 - Annals of Pure and Applied Logic 156 (2):210-244.
    We study Dedekind cuts on ordered Abelian groups. We introduce a monoid structure on them, and we characterise, via a suitable representation theorem, the universal part of the theory of such structures.
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  • Definable Functions Continuous on Curves in o-Minimal Structures.Janak Ramakrishnan - 2014 - Annals of Pure and Applied Logic 165 (7-8):1339-1351.
    We give necessary and sufficient conditions on a non-oscillatory curve in an o-minimal field such that, for any bounded definable function, the germ of the function on an initial segment of the curve has a definable extension to a closed set. This situation is translated into a question about types: What are the conditions on an n-type such that, for any bounded definable function, the germ of the function on the type has a definable continuous global extension? Certain categories of (...)
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  • Uniform Bounds on Growth in o-Minimal Structures.Janak Ramakrishnan - 2010 - Mathematical Logic Quarterly 56 (4):406-408.
    We prove that a function definable with parameters in an o-minimal structure is bounded away from ∞ as its argument goes to ∞ by a function definable without parameters, and that this new function can be chosen independently of the parameters in the original function. This generalizes a result in [1]. Moreover, this remains true if the argument is taken to approach any element of the structure , and the function has limit any element of the structure.
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