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Real structures on minimal ruled surfaces
In this paper, we give a complete description of the deformation classes of
real structures on minimal ruled surfaces. In particular, we show that these
classes are determined by the topology of the real structure, which means that
real minimal ruled surfaces are quasi-simple. As an intermediate result, we
obtain the classification, up to conjugation, of real structures on
decomposable ruled surfaces.Comment: 24 pages, 3 figure
Uniform bounds on growth in o-minimal structures
We prove that a function definable with parameters in an o-minimal structure
is bounded away from infinity as its argument goes to infinity 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 a paper of Friedman and Miller. Moreover, this remains true if the
argument is taken to approach any element of the structure (or plus/minus
infinity), and the function has limit any element of the structure (or
plus/minus infinity).Comment: 3 pages. To appear in Mathematical Logic Quarterl
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