TRAVELING SAFELY IN THE MULTIVERSE FOR SUPERCOMPACTNESS
Posted: January 16, 2020 (from a document made Fall 2012)
This document was written before my oral exam at CUNY. It is about forcing to preserve supercompactness via the Lottery Preparation or Lottery Preparation. If it helps anyone, that is great. Comments at twitter @erincarmody5
Recently submitted papers
Posted: June 1, 2019
I would like to share 3 papers which I recently submitted for publication.
The first paper explores a way to express the natural numbers as unique structures created from prime blocks. I use general idea to create structures for Fibonacci numbers.
The second paper explores a new way to visualize complex functions in 3D.
Here is the abstract for the third paper: This paper is a continuation of "Killing Them Softly: Degrees of Inaccessible and Measurable Cardinals", and follows the theme up the large cardinal hierarchy to force to distinguish between its subtle degrees. The first main theorem shows how to force a measurable cardinal to have a desired maximal Mitchell rank. As for measurable cardinals, an analogous rank to Mitchell rank is defined for supercompactness embeddings. The second main theorem shows how to softly kill between degrees of supercompact cardinals (and provides the reader with the details of classic lifting arguments). Also, many results about supercompact and strongly compact cardinals are collected here which follow the theme, such as Magidor's identity crisis.
Expressing natural numbers
Killing them softly Vol. 2: Measurable to Supercompact and beyond
Set Theory: from Cantor to Cohen and beyond
Posted: April 19, 2019
Update: The talk is tomorrow 4/23
Killing Them Softly: Degrees of Inaccessible and Mahlo Cardinals
Mathematical Logic Quarterly: Volume 63, Issue 3-4, November 2017, pages 256-264
Posted: April 15, 2019
This is my first paper, which was based on the first half of my PhD thesis. This paper introduces the theme of killing‐them‐softly between set‐theoretic universes. The main theorems show how to force to reduce the large cardinal strength of a cardinal to a specified desired degree. The killing‐them‐softly theme is about both forcing and the gradations in large cardinal strength. Thus, I also develop meta‐ordinal extensions of the hyper‐inaccessible and hyper‐Mahlo degrees. This paper extends the work of Mahlo to create new large cardinals and also follows the larger theme of exploring interactions between large cardinals and forcing central to modern set theory.