Reflection principles in subsystems of analysis

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• Emanuele Frittaion, University of Leeds
• Friday 23 November 2018, 10:30-11:30
• Computer Science, The Sloman Lounge (UG).

If you have a question about this talk, please contact Noam Zeilberger.

The study of reflection principles goes back to Feferman “Transfinite recursive progressions of axiomatic theories” (1962), and originates from Turing (PhD) thesis “Systems of logic based on ordinals” (1938). Worth of mention is the work of Schmerl and Beklemishev. Long story short, we know a lot about reflection in first order arithmetic. If we look at analysis (classical second order arithmetic), we hardly have the same picture. In the context of analysis, people have studied omega-model reflection (Friedman, Simpson, Jager and Strahm) and well-ordering principles (Rathjen, Weiermann, Afshari, Montalban, Marcone and others). Yet the big question remains: what reflection principles, if any, give a precise measure of the proof-theoretic strength of a given subsystem of analysis? Spoiler: The big question will not be answered in this talk.

This talk is part of the Theoretical computer science seminar series.

This talk is included in these lists:

• Computer Science Departmental Series
• Computer Science Distinguished Seminars
• Computer Science, The Sloman Lounge (UG)
• Theoretical computer science seminar
• computer sience

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