Laczkovich proved from ZF that, given a countable sequence of Borel sets on a perfect Polish space, if the limit superior along every subsequence was uncountable, then there was a particular subsequence whose intersection actually contained a perfect subset. Komjath later expanded the result to hold for analytic sets. In this paper, by adding AD and sometimes V=L(R) to our assumptions, we will extend the result further. This generalization will include the increasing of the length of the sequence to certain uncountable regular cardinals as well as removing any descriptive requirements on the sets.
| Identifer | oai:union.ndltd.org:unt.edu/info:ark/67531/metadc271913 |
| Date | 05 1900 |
| Creators | Walker, Daniel |
| Contributors | Jackson, Stephen, Brozovic, Douglas, Gao, Su |
| Publisher | University of North Texas |
| Source Sets | University of North Texas |
| Language | English |
| Detected Language | English |
| Type | Thesis or Dissertation |
| Format | Text |
| Rights | Public, Walker, Daniel, Copyright, Copyright is held by the author, unless otherwise noted. All rights Reserved. |
Page generated in 0.0022 seconds