Special Session
The strength of versions of Mycielski’s Theorem
Online
Mycielski’s Theorem is a Ramsey-theoretic result on the reals with versions for measure and for category. These imply respectively that there is a perfect tree whose paths are all relatively 1-random, and that there is a perfect tree whose paths are all relatively 1-generic. In fact, in relativized form, the latter two statements are equivalent to the two versions of Mycielski’s Theorem. I will discuss joint work with Carl G. Jockusch, Jr. and Paul E. Schupp on the computability-theoretic and reverse-mathematical strength of these statements.
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