Skip to main content Accessibility help
×
Home

ONE DIMENSIONAL T.T.T STRUCTURES

  • DANIEL LOWENGRUB (a1)

Abstract

In this paper we analyze the relationship between o-minimal structures and the notion of ω-saturated one-dimensional t.t.t structures. We prove that if removing any point from such a structure splits it into more than one definably connected component then it must be a one-dimensional simplex of a finite number of o-minimal structures. In addition, we show that even if removing points doesn’t split the structure, additional topological assumptions ensure that the structure is locally o-minimal. As a corollary we obtain the result that if an ω-saturated one-dimensional t.t.t structure admits a topological group structure then it is locally o-minimal. We also prove that the number of connected components in a definable family is uniformly bounded, which implies that an elementary extension of an ω-saturated one-dimensional t.t.t structure is t.t.t as well.

Copyright

References

Hide All
[1]Pillay, A., First order topological structures and theories, this Journal, vol. 52 (1987), no. 3, pp. 763778.
[2]Robinson, A., A note on topological model theory, Fundamenta Mathematicae, vol. 81 (1974), pp. 159171.
[3]Whyburn, G. T., Analytic Topology, American Mathematical Society, Colloquium Publications, New York, vol. 28, 1942, ch. 3, pp. 4164.

Keywords

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed