To send content items to your account,
please confirm that you agree to abide by our usage policies.
If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account.
Find out more about sending content to .
To send content items to your Kindle, first ensure email@example.com
is added to your Approved Personal Document E-mail List under your Personal Document Settings
on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part
of your Kindle email address below.
Find out more about sending to your Kindle.
Note you can select to send to either the @free.kindle.com or @kindle.com variations.
‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi.
‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.
We formulate and prove (in ZFC) a strong coloring theorem which holds at successors of singular cardinals, and use it to answer several questions concerning Shelah's principle Pr1 (μ+, μ+, μ+, cf (μ)) for singular μ.
The ninth Appalachian Set Theory workshop was held at the Fields Institute in Toronto on May 29–30, 2009. The lecturers were Todd Eisworth and Justin Moore. As a graduate student David Milovich assisted in writing this chapter, which is based on the workshop lectures.
The notes which follow reflect the content of a two day tutorial which took place at the Fields Institute on 5/29 and 5/30 in 2009. Most of the content has existed in the literature for some time (primarily in the original edition of ) but has proved difficult to read and digest for various reasons. The only new material contained in these lectures concerns the notion of a fusion scheme presented in Sections 6 and 7 and even this has more to do with style than with mathematics. Our presentation of the iteration theorems follows . The k-iterability condition is a natural extrapolation of what appears in  and , where the iteration theorem for the ℵ0-iterability condition is presented (with a weakening of < ω1-properness). The formulation of complete properness is taken from . We stress, however, these definitions and theorems are really technical and/or stylistic modifications of the theorems and definitions of Shelah presented in . Those interested in further reading on the topic of the workshop should consult: , , , , , and . We would like to thank Ilijas Farah, Miguel Angel Mota, Paul Shafer, and the anonymous referee for their careful reading and suggesting a number of improvements.
In this paper, we investigate the extent to which techniques used in , , and —developed to prove coloring theorems at successors of singular cardinals of uncountable cofinality—can be extended to cover the countable cofinality case.
We investigate the effect of a variant of Matet forcing on ultrafilters in the ground model and give a characterization of those P–points that survive such forcing, answering a question left open by Blass . We investigate the question of when this variant of Matet forcing can be used to diagonalize small filters without destroying P–points in the ground model. We also deal with the question of generic existence of stable ordered-union ultrafilters.
Email your librarian or administrator to recommend adding this to your organisation's collection.