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DTSTAMP:20241004T123644
DTSTART;TZID=America/Detroit:20241007T130000
DTEND;TZID=America/Detroit:20241007T140000
SUMMARY:Lecture / Discussion:Student Logic and History of Math Seminar (Invited Address): Provability Logic
DESCRIPTION:Provability logic seeks to efficiently describe\, by suitable axioms and rules of inference\, what a reasonable theory can prove about its own provability predicate. Here “reasonable” means that the theory can prove basic facts about the natural numbers\; Peano arithmetic is more than enough.\n\nThe notation used in provability logic (meaning in the particular provability logic that I’ll concentrate on) is the same as in most modal logics\, namely ordinary propositional logic plus a modal operator\, written as a box. But the box operator has the unusual interpretation “it is provable that”. It turns out that this provability logic can be axiomatized by adding to ordinary propositional logic just one axiom (schema) and one inference rule. The rule is very simple\, but the axiom expresses Löb’s theorem\, a far from obvious fact about provability.\n\nI’ll begin by explaining Löb’s theorem. Then I’ll discuss the axiomatic system of provability logic and a few proofs in that system. Next\, I’ll describe the Kripke models of provability logic. Finally\, I’ll discuss two completeness theorems for this logic\, one saying that Kripke models provide a complete semantics\, and the other saying that provability logic exactly captures what a reasonable theory can prove about its own provability.
UID:126576-21857352@events.umich.edu
URL:https://events.umich.edu/event/126576
CLASS:PUBLIC
STATUS:CONFIRMED
CATEGORIES:Graduate Students,Mathematics,seminar,Talk,Undergraduate Students
LOCATION:East Hall - 3866
CONTACT:
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BEGIN:VEVENT
DTSTAMP:20240904T181854
DTSTART;TZID=America/Detroit:20241007T132000
DTEND;TZID=America/Detroit:20241007T135000
SUMMARY:Performance:Tiffany Ng\, carillon
DESCRIPTION:University Carillonist Tiffany Ng performs on the Ann & Robert H. Lurie Carillon\, an instrument of 60 bells with the lowest bell (bourdon) weighing 6 tons.\n\nThirty-minute recitals are performed on the Lurie Carillon every weekday that classes are in session. During these recitals\, visitors may take the elevator to level 2 to view the largest bells\, or to level 3 to see the carillonist performing. (Visitors subject to acrophobia are recommended to visit level 2 only.) An optional spiral stairway between levels 2 and 3 allows for up-close views of some of the largest bells.
UID:125711-21855657@events.umich.edu
URL:https://events.umich.edu/event/125711
CLASS:PUBLIC
STATUS:CONFIRMED
CATEGORIES:Faculty,Free,Music,North Campus,Talk
LOCATION:Lurie Ann & Robert H. Tower
CONTACT:
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