# Reflection Principles Involving Provability and Explicit Proofs

## Elena Nogina

### The City University of New York

Reflection principles are classical objects in proof theory and the areas studying GĂ¶del’s Incompleteness. Reflection principles based on provability predicates were introduced in the 1930s by Rosser and Turing, and later were explored by Feferman, Kreisel & Levi, Schmerl, Artemov, Beklemishev and others.

We study reflection principles of Peano Arithmetic involving both Proof and Provability predicates. We find a classification of these principles and establish their linear ordering with respect to their metamathematical strength.

Dr. Elena Y. Nogina has authored more than sixty papers in mathematical logic and computability theory. She was a tenured professor for many years at Moscow University. She also held a research position at the Computing Center of the USSR Academy of Sciences, as well as visiting professorships at the University of Montpellier, France, and at the University of Amsterdam, the Netherlands. Since moving to the United States, Dr. Nogina has been teaching mathematics at CUNY, first at Lehman College and then at BMCC. Her current research interests include modal logics of provability and proofs, and their applications in the mathematical theory of knowledge and game theory. Since her appointment to BMCC in 2004, Dr. Nogina has been the recipient of research grants from different agencies, including the National Science Foundation. She was recently a visiting scholar at the University of Bern, Switzerland, and Cornell University.