Monthly Archives: February 2012

MA and its effect on Tree Partitions

(This is the presentation I gave for Stevo Todorcevic’s course Combinatorial Set Theory on Feb 28, 2012. The material comes from Stevo’s 1983 paper “Partition Relations for Partially Ordered Sets”.) In partition relations for ordinals, it has been established that: Theorem (Erdos-Rado). $\omega_1 \rightarrow (\omega_1, \omega+1)^2$ Later it was shown that this is the best […]

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The Delta-System Lemma

Now that you know the basics of countable elementary submodels (CESM), you might think that you are in the clear. “Mike”, you say arrogantly, “I know all the most basic properties of CESMs, without proof I remind you, what else could I possibly want?”. I gently and patiently remind you that CESMs are worthless unless […]

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