Lecture Title: Some theorems are more equal than others: a slow introduction to Reverse Mathematics
Speaker: Dr. Sam Sanders (Technical University of Darmstadt, Germany)
Date and Time: 17 November 2020, 7pm-9pm Beijing time (11am-1pm UTC)
Commentator: Prof. Yue Yang (National University of Singapore, Singapore)
Organizer: School of Philosophy, Wuhan University
From high school mathematics to research level literature, we can easily find statements like“Theorem A is stronger than Theorem B” and “These two formulas are equivalent". The field Reverse Mathematics provides a framework for making such statements precise, based on mathematical logic. I will provide a gentle introduction to this field and discuss some new directions based on my own research.
About the speaker:
Sam Sanders’ research is part of mathematical logic, computability and proof theory in particular. He investigates the role of the uncountable in these disciplines as follows: (1) studying mathematics in logic means chosing (often countable) representations/codes for classes of objects. Where does this coding practise break down for the uncountable? (2) What is the right scale for classifying objects? Is the Hilbert-Bernays inspired "Goedel hierarchy" based on comprehension the right one? (3) What are the foundational implications of logic? For instance, can they provide evidence for e.g. Platonism?
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