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Faculty
schimmerling
Ernest Schimmerling, Professor
Ph.D., University of California, Los Angeles
E-mail: eschimme@andrew.cmu.edu
Office: Wean Hall 7125
Phone: 412-268-5913
Personal web site

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.

Selected Publications:

  • E. Schimmerling, "The ABC's of mice", to appear in Bull. Symbolic Logic.
  • J. Cummings and E. Schimmerling, "Indexed squares", to appear in Israel J. Math.
  • E. Schimmerling, "Woodin cardinals, Shelah cardinals, and the Mitchell-Steel core model", to appear in Proc. Amer. Math. Soc.
  • E. Schimmerling and M. Zeman, "Square in core models", to appear in Bull. Symbolic Logic.
  • E. Schimmerling and W.H. Woodin, "The Jensen covering property", to appear in J. Symbolic Logic.
  • E. Schimmerling, "A finite family weak square principle", J. Symbolic Logic 64 (1999) 1087–1110.
  • E. Schimmerling, "Covering properties of core models", Sets and Proofs (Leeds, 1997), 281–299, London Math. Soc. Lecture Note Ser. 258, Cambridge Univ. Press, Cambridge, 1999.
  • E. Schimmerling and J.R. Steel, "The maximality of the core model", Trans. Amer. Math. Soc. 351 (1999) 3119–3141.
  • E. Schimmerling, "Combinatorial set theory and inner models", Set theory (Curacao 1995 and Barcelona 1996), 207–212, Kluwer Acad. Publ., Dordrecht, 1998.
  • W.J. Mitchell, E. Schimmerling and J.R. Steel, "The covering lemma up to a Woodin cardinal", Ann. Pure Appl. Logic 84 (1997) 219–255.
  • E. Schimmerling and J.R. Steel, "Fine structure for tame inner models", J. Symbolic Logic 61 (1996) 621–639.
  • W.J. Mitchell and E. Schimmerling, "Weak covering without countable closure", Math. Res. Lett. 2 (1995) 595–609.
  • E. Schimmerling, "Combinatorial principles in the core model for one Woodin cardinal", Ann. Pure Appl. Logic 74 (1995) 153–201.