About

Ernest Schimmerling is a Professor in the Department of Mathematical Sciences at Carnegie Mellon University, located in Wean Hall, Pittsburgh. He holds a Ph.D. from the University of California, Los Angeles, and has completed postdoctoral appointments at the University of California, Berkeley, the Massachusetts Institute of Technology, and the University of California, Irvine. His research focuses on set theory, a branch of mathematical logic, with particular emphasis on the hierarchy of large cardinal axioms, also known as strong axioms of infinity. These large cardinals are applied across various areas of mathematics to address questions that are otherwise independent. Professor Schimmerling is especially interested in techniques for constructing inner models for large cardinals that generalize Gödel's Constructible Universe. His work also explores connections between inner model theory and descriptive set theory, infinitary combinatorics, cardinal arithmetic, and forcing. His contributions have advanced understanding in these areas, and he has published extensively on topics related to large cardinals, inner models, and related set-theoretic concepts.

Research topics

• Computer Science
• Mathematical analysis
• Combinatorics
• Mathematics
• Discrete mathematics

Selected publications

• Maximal Prikry Sequences

  Open MIND · 2026-01-30

  preprint1st authorCorresponding

  In this paper we investigate the covering machinery of the Jensen-Steel core model $K$, under the hypothesis that there is no inner model with a Woodin cardinal. In an earlier work, Mitchell and the first author showed that if $ν>ω_2$ is a regular cardinal in $K$ but a singular ordinal in $V$, then $ν$ is a measurable cardinal in $K$. In this article, we further show that under certain circumstances, there exists a maximal Prikry sequence $C$ for a measure on $ν$ in $K$. The first author shows that the anti-large cardinal hypothesis is necessary. In a more restrictive setting, we prove that every subset of $ν$ with size $<|ν|$ can be covered by a set in $K[C]$ with size $<|ν|$. Benhamou and the first author show that the result is optimal.

  DOI

• Maximal Prikry Sequences

  arXiv (Cornell University) · 2026-01-30

  articleOpen access1st authorCorresponding

  In this paper we investigate the covering machinery of the Jensen-Steel core model $K$, under the hypothesis that there is no inner model with a Woodin cardinal. In an earlier work, Mitchell and the first author showed that if $ν>ω_2$ is a regular cardinal in $K$ but a singular ordinal in $V$, then $ν$ is a measurable cardinal in $K$. In this article, we further show that under certain circumstances, there exists a maximal Prikry sequence $C$ for a measure on $ν$ in $K$. The first author shows that the anti-large cardinal hypothesis is necessary. In a more restrictive setting, we prove that every subset of $ν$ with size $<|ν|$ can be covered by a set in $K[C]$ with size $<|ν|$. Benhamou and the first author show that the result is optimal.

  PublisherOA PDF

• Covering at limit cardinals of <i>K</i>

  Journal of Mathematical Logic · 2023

  Senior authorCorresponding
  • Mathematics
  • Combinatorics
  • Discrete mathematics

  Assume that there is no transitive class model of [Formula: see text] with a Woodin cardinal. Let [Formula: see text] be a singular ordinal such that [Formula: see text] and [Formula: see text]. Suppose [Formula: see text] is a regular cardinal in K. Then [Formula: see text] is a measurable cardinal in K. Moreover, if [Formula: see text], then [Formula: see text].

  PublisherDOI

• NOTICES

  Bulletin of Symbolic Logic · 2020

  • Computer Science
  • Computer Science

  An abstract is not available for this content so a preview has been provided. As you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

  DOI

• BSL volume 24 issue 4 Cover and Front matter

  Bulletin of Symbolic Logic · 2018-12-01

  articleOpen access

  An abstract is not available for this content so a preview has been provided. As you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

  PublisherOA PDFDOI

• BSL volume 22 issue 1 Cover and Front matter

  Bulletin of Symbolic Logic · 2016-03-01

  articleOpen access

  of ideas among mathematicians, computer scientists, linguists, and others interested in this fi eld.

  PublisherOA PDFDOI

• John R. Steel and W. Hugh Woodin, <i>HOD as a core model</i>, Ordinal Definability and Recursion Theory: The Cabal Seminar, <b><i>vol. III</i></b> (A. S. Kechris, B. Löwe, and J. R. Steel, editors), Lecture Notes in Logic 43, Association for Symbolic Logic and Cambridge University Press, 2016, pp. 257–343.

  Bulletin of Symbolic Logic · 2016-12-01

  article1st authorCorresponding

  John R. Steel and W. Hugh Woodin, HOD as a core model, Ordinal Definability and Recursion Theory: The Cabal Seminar, vol. III (A. S. Kechris, B. Löwe, and J. R. Steel, editors), Lecture Notes in Logic 43, Association for Symbolic Logic and Cambridge University Press, 2016, pp. 257–343. - Volume 22 Issue 4

  PublisherDOI

• BSL volume 22 issue 4 Cover and Front matter

  Bulletin of Symbolic Logic · 2016-12-01

  articleOpen access

  An abstract is not available for this content so a preview has been provided. As you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

  PublisherOA PDFDOI

• BSL volume 21 issue 3 Cover and Front matter

  Bulletin of Symbolic Logic · 2015-09-01

  articleOpen access

  of ideas among mathematicians, computer scientists, linguists, and others interested in this fi eld.

  PublisherOA PDFDOI

• BSL volume 21 issue 1 Cover and Front matter

  Bulletin of Symbolic Logic · 2015-03-01

  articleOpen access

  of ideas among mathematicians, computer scientists, linguists, and others interested in this fi eld.

  PublisherOA PDFDOI

Recent grants

• Core Models and Combinatorial Set Theory

  NSF · $104k · 2004–2007

• Core Models and Combinatorial Set Theory

  NSF · $116k · 2007–2010

Frequent coauthors

• Thierry Coquand

  University of Gothenburg

  1665 shared

• Patricia Blanchette

  1665 shared

• Frank R. Wagner

  Max Planck Society

  1665 shared

• Andrea Cantini

  University of Florence

  1665 shared

• Leonid Libkin

  1665 shared

• André Nies

  1452 shared

• Mark Colyvan

  University of Sydney

  1302 shared

• Menachem Kojman

  Ben-Gurion University of the Negev

  1302 shared

Education

• Ph.D.

  University of California, Los Angeles

• Other

  University of California, Berkeley

• Other

  Massachusetts Institute of Technology

• Other

  University of California, Irvine