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The Structure Of Models Of Second-Order Set Theories, Kameryn J. Williams
The Structure Of Models Of Second-Order Set Theories, Kameryn J. Williams
Dissertations, Theses, and Capstone Projects
This dissertation is a contribution to the project of second-order set theory, which has seen a revival in recent years. The approach is to understand second-order set theory by studying the structure of models of second-order set theories. The main results are the following, organized by chapter. First, I investigate the poset of T-realizations of a fixed countable model of ZFC, where T is a reasonable second-order set theory such as GBC or KM, showing that it has a rich structure. In particular, every countable partial order embeds into this structure. Moreover, we can arrange so that these embedding preserve …