Presented By: Student Logic and History of Math Seminar  Department of Mathematics
Student Logic and History of Math Seminar (Invited Address): Degrees of (un)definability
Professor Ronnie Chen
In calculus, one learns several subtle "pathologies" involving the real number line, such as convergent but not absolutely convergent infinite series, differentiable functions with discontinuous derivative, and infinitelydifferentiable functions whose Taylor series has zero radius of convergence. A little thought reveals that some of these concepts seem to be much more complicated than others. For example, while in calculus one learns to approximately "check" if a function is continuously differentiable (just draw a graph and zoom in!), it seems absolutely hopeless to check plain differentiability in any systematic way.
This talk will give a gentle introduction to Descriptive Set Theory, a subfield of mathematical logic providing the tools to make such statements precise, which can be variously thought of as "infinitary propositional logic", "lowlevel set theory", "real analysis without approximations", or "computability modulo countable uncomputability".
This talk will give a gentle introduction to Descriptive Set Theory, a subfield of mathematical logic providing the tools to make such statements precise, which can be variously thought of as "infinitary propositional logic", "lowlevel set theory", "real analysis without approximations", or "computability modulo countable uncomputability".
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