Creature Forcing and Topological Ramsey Spaces
Creature forcing, Topological Ramsey spaces, Product tree Ramsey theorem, Ultrafilter
College of Natual Science and Mathematics, Mathematics
This article introduces a line of investigation into connections between creature forcings and topological Ramsey spaces. Three examples of sets of pure candidates for creature forcings are shown to contain dense subsets which are actually topological Ramsey spaces. A new variant of the product tree Ramsey theorem is proved in order to obtain the pigeonhole principles for two of these examples.
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Dobrinen, Natasha. “Creature Forcing and Topological Ramsey Spaces.” Topology and Its Applications, vol. 213, 2016, pp. 110–126. doi: 10.1016/j.topol.2016.08.008.