James Cummings

Associate Professor
Ph.D., Cambridge University

Office: Wean Hall 7101
Phone: (412) 268-2551
E-mail: jcumming@andrew.cmu.edu
Personal web site

Research

My research interests lie in set theory, with a focus on large cardinals, forcing and inner models. A major theme in modern set theory is the determination of the "consistency strength" of combinatorial statements; typically this strength is measured by a large cardinal axiom, with forcing used to show the axiom is sufficient and inner models used to show that it is necessary. I am also interested in purely combinatorial questions, and in applications of set theory to areas such as algebra and analysis.

Selected Publications

Cummings, James and Foreman, Matthew and Magidor, Menachem Squares, scales and stationary reflection, Journal of Mathematical Logic 1 (2001), no 1, 35–98

Apter, Arthur and Cummings, James: A global version of a theorem of Ben-David and Magidor. Ann. Pure Appl. Logic 102 (2000), no. 3, 199–222.

Cummings, James and Shelah, Saharon: Some independence results on reflection. J. London Math. Soc. (2) 59 (1999), no. 1, 37–49.

Cummings, James & Foreman, Matthew: The tree property. Adv. Math. 133 (1998), no. 1, 1–32.

Cummings, James: Souslin trees which are hard to specialise. Proc. Amer. Math. Soc. 125 (1997), no. 8, 2435–2441.

Cummings, James: Collapsing successors of singulars. Proc. Amer. Math. Soc. 125 (1997), no. 9, 2703–2709.

Cummings, James & Shelah, Saharon: Cardinal invariants above the continuum. Ann. Pure Appl. Logic 75 (1995), no. 3, 251–268.

Cummings, James: Strong ultrapowers and long core models. J. Symbolic Logic 58 (1993), no. 1, 240–248.

Cummings, James: A model in which GCH holds at successors but fails at limits. Trans. Amer. Math. Soc. 329 (1992), no. 1, 1–39.

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