# Ernest Schimmerling

## Professor

**Address:**

7125 Wean Hall

Department of Mathematical Sciences

Carnegie Mellon University

5000 Forbes Avenue

Pittsburgh, PA 15213

**P:** 412-268-5913

# Education

Ph.D., University of California, Los Angeles

Postdoctoral Appointments:

- University of California, Berkeley
- Massachusetts Institute of Technology
- University of California, Irvine

# Research

My area of research is set theory, which is a branch of mathematical logic. Many of my results concern the hierarchy of large cardinal axioms, which are also called strong axioms of infinity. Large cardinals have been applied in many areas of mathematics, not just logic, to answer otherwise independent questions.

I am particularly interested in techniques for building inner models for large cardinals in ways that generalize Goedel’s Constructible Universe. I have also worked on connections between inner model theory and descriptive set theory, infinitary combinatorics, cardinal arithmetic and forcing.

# Select Publications

Mitchell, W.J. and Schimmerling, E. (1995). Weak covering without countable closure. *Mathematical Research Letters,* 2, 595-609.

Mitchell, W.J., Schimmerling, E. and Steel, J.R. (1997). The covering lemma up to a Woodin cardinal. *Annals of Pure and Applied Logic, *84, 219-255.

Schimmerling, E. and Steel, J.R. (1999). The maximality of the core model. *Transactions of the American Mathematical Society*, 351, 3119-3141.

Cummings, J. and Schimmerling, E. (2002). Indexed squares. *Israel Journal of Mathematics*, 131, 61-99.

Schimmerling, E. and Zeman, M. (2004). Characterization of **□ _{X}** in core models.

*Journal of Mathematical Logic*, 4, 1-72.

Schimmerling, E. (2007). Coherent sequences and threads. *Advances in Mathematics*, 216, 89-117.

Jensen, R., Schimmerling, E., Schindler, R. and Steel, J. (2009). Stacking mice. *The Journal of Symbolic Logic,* 74, 315-335.

Krueger, J. and Schimmerling, E. (2011). An equiconsistency result on partial squares. *Journal of Mathematical Logic*, 11, 29-59.

Krueger, J. and Schimmerling, E. (2014). Separating weak partial square principles. *Annals of Pure and Applied Logic*, 165, 609-619.