Lexi Fitzmaurice, PhD Student
Mathematics
Advisor: Dr. Daniel Herden
What is true? In mathematics, the answer seems to be unambiguous, as questions of truth can be settled through the formalistic process of proof. However, this is far from the full story. In 1938, Kurt Godel shocked the intellectual world with the discovery that truth and provability are not as inseparable as had been originally assumed. In this gap between what is mathematically true and mathematically provable, a number of deep and mysterious results arise concerning the nature of computation, the definability of truth, the size of the infinite, and the limitations of formal reasoning itself. By identifying those mathematical statements whose truth is absolute, and those whose truth depends upon the model taken, we can force certain mathematical objects to have prescribed properties by modifying the model in which we evaluate them. In particular, we use this forcing technique to make Aleph-1-free groups free, which opens the door to a number of novel algebraic insights, and deepens our understanding of the set-theoretical multiverse.
Tuesday, 24 February 2020, 3:30 – 4:30 pm, BSB, room C.206.
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