# The Foundational Impact of Recursion Theory

In honor of Steve Simpson's 70th birthday
University of Connecticut at Storrs
May 22, 2016

Recursion theory has many deep applications to the foundations of mathematics. This conference aims to bring together researchers working in all aspects and foundational applications of recursion theory. The conference is in honor of Steve Simpson's 70th birthday.

## Steve Simpson

Stephen G. Simpson earned a PhD from Massachusetts Institute of Technology in 1971, advised by Gerald Sacks. Simpson held positions at Yale University, the University of California at Berkeley, and the University of Oxford before taking a permanent position at Pennsylvania State University in 1975. He has published 95+ papers and five books, including the seminal Subsystems of Second-Order Arithmetic. His research topics have included recursion theory, second-order arithmetic, Reverse Mathematics, intuitionism, mass problems, randomness, dynamical systems, and philosophy of mathematics. He has supervised 20 PhD students, of whom 12 have subsequently earned tenure as professors of mathematics.

## PhD students

• John Steel,[1] Determinateness and Subsystems of Analysis, Berkeley, 1977
• Rick Smith, Theory of Profinite Groups with Effective Presentations, Penn State, 1979
• Galen Weitkamp, Kleene Recursion over the Continuum, Penn State, 1980
• Peter Pappas, The Model Theoretic Structure of Group Rings, Penn State, 1982
• Stephen Brackin, On Ramsey-type Theorems and their Provability in Weak Formal Systems, Penn State, 1984
• Mark Legrand, Coanalytic Sets in the Absence of Analytic Determinacy, Penn State, 1985
• Douglas Brown, Functional Analysis in Weak Subsystems of Second Order Arithmetic, Penn State, 1987
• Jeffry Hirst, Combinatorics in Subsystems of Second Order Arithmetic, Penn State, 1987
• Xiaokang Yu, Measure Theory in Weak Subsystems of Second Order Arithmetic, Penn State, 1987
• Fernando Ferreira, Polynomial Time Computable Arithmetic and Conservative Extensions, Penn State, 1988
• Kostas Hatzikiriakou, Commutative Algebra in Subsystems of Second Order Arithmetic, Penn State, 1989
• Alberto Marcone, Foundations of BQO Theory and Subsystems of Second Order Arithmetic, Penn State, 1993
• A. James Humphreys, On the Necessary Use of Strong Set Existence Axioms in Analysis and Functional Analysis, Penn State, 1996
• Mariagnese Giusto, Topology, Analysis, and Reverse Mathematics, Università di Torino, 1998
• Stephen Binns, The Medvedev and Muchnik Lattices of $\, \Pi^0_1$ Classes, Penn State, 2003
• Carl Mummert, On the Reverse Mathematics of General Topology, Penn State, 2005
• W. M. Phillip Hudelson, Scaled Randomness and Kolmogorov Complexity, Penn State, 2013
• Noopur Pathak, Computable Aspects of Measure Theory, Penn State, 2013
• Sankha S. Basu, A Model of Intuitionistic Higher-Order Logic Based on the Turing Degrees, Penn State, 2013
• Adrian Maler, Effective Theory of Lévy and Feller Processes, Penn State, 2015

## Postdocs

• Kazuyuki Tanaka, Penn State, 1990
• Takeshi Yamazaki, Penn State, 2000
• Natasha Dobrinen, Penn State, 2001–2004
• Rebecca Weber, Penn State, 2004
• Keita Yokoyama, Penn State, 2011
• Jason Rute, Penn State, 2013–2016

↑ [1]: Although Steel's official thesis adviser was Professor John Addison of Berkeley, the following is a quotation from the acknowledgements page of Steel's thesis. "I owe a great debt to Stephen Simpson, who guided me expertly in the perilous transition from study to research. The results of Chapters 1 and 2, together with less tangible aspects of my research, are a product of Simpson's influence." The thesis consists of three chapters.