A Two-Cardinal Ramsey Operator on Ideals

Philip White (George Washington University)

03-Nov-2022, 18:00-19:00 (2 years ago)

Abstract: Let II be a κ\kappa-complete ideal on κ\kappa. Similar to the one-cardinal ineffability operator of Baumgartner, Feng defined a one-cardinal Ramsey operator on II. A basic result of Feng is applying the one cardinal Ramsey operator to II yields a normal ideal. Feng also showed under what conditions the ideal given by applying the Ramsey operator is equivalently generated by a “pre-Ramsey” ideal as well as the Πn+11\Pi^1_{n+1} indescribability ideal. Finally Feng showed iterated use of the one-cardinal Ramsey operator forms a proper hierarchy. Feng was able to show these results for <κ+< \kappa+ iterations of the one-cardinal Ramsey operator by utilizing canonical functions. Similar to other results of Brent Cody and the presenter, these results in the one-cardinal setting can be generalized to a two-cardinal setting. The theorems of Feng will be discussed in detail as well as the analogous two-cardinal versions of Brent Cody and the presenter.

logic

Audience: researchers in the topic


Online logic seminar

Series comments: Description: Seminar on all areas of logic

Organizer: Wesley Calvert*
*contact for this listing

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