{ "126576-21857352": { "datetime_modified":"20241004T123644", "datetime_start":"20241007T130000", "datetime_end":"20241007T140000", "has_end_time":1, "date_start":"2024-10-07", "date_end":"2024-10-07", "time_start":"13:00:00", "time_end":"14:00:00", "time_zone":"America\/Detroit", "event_title":"Student Logic and History of Math Seminar (Invited Address): Provability Logic", "occurrence_title":"", "combined_title":"Student Logic and History of Math Seminar (Invited Address): Provability Logic: Professor Andreas Blass", "event_subtitle":"Professor Andreas Blass", "event_type":"Lecture \/ Discussion", "event_type_id":"13", "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 \u201creasonable\u201d means that the theory can prove basic facts about the natural numbers; Peano arithmetic is more than enough.\r\n\r\nThe notation used in provability logic (meaning in the particular provability logic that I\u2019ll 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 \u201cit is provable that\u201d.\u00a0It 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 L\u00f6b\u2019s theorem, a far from obvious fact about provability.\r\n\r\nI\u2019ll begin by explaining L\u00f6b\u2019s theorem. Then I\u2019ll discuss the axiomatic system of provability logic and a few proofs in that system. Next, I\u2019ll describe the Kripke models of provability logic.\u00a0Finally, I\u2019ll 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.", "occurrence_notes":null, "guid":"126576-21857352@events.umich.edu", "permalink":"http:\/\/events.umich.edu\/event\/126576", "building_id":"1000166", "building_name":"East Hall", "campus_maps_id":"53", "room":"3866", "location_name":"East Hall", "has_livestream":0, "cost":"", "tags":["Graduate Students","Mathematics","seminar","Talk","Undergraduate Students"], "website":"", "sponsors":[ { "group_name":"Department of Mathematics", "group_id":"3791", "website":"" } ], "image_url":"", "styled_images":{ "event_thumb":"", "event_large":"", "event_large_2x":"", "event_large_lightbox":"", "group_thumb":"", "group_thumb_square":"", "group_large":"", "group_large_lightbox":"", "event_large_crop":"", "event_list":"", "event_list_2x":"", "event_grid":"", "event_grid_2x":"", "event_feature_large":"", "event_feature_thumb":"" }, "occurrence_count":1, "first_occurrence":21857352 } , "125711-21855657": { "datetime_modified":"20240904T181854", "datetime_start":"20241007T132000", "datetime_end":"20241007T135000", "has_end_time":1, "date_start":"2024-10-07", "date_end":"2024-10-07", "time_start":"13:20:00", "time_end":"13:50:00", "time_zone":"America\/Detroit", "event_title":"Tiffany Ng, carillon", "occurrence_title":"", "combined_title":"Tiffany Ng, carillon", "event_subtitle":"", "event_type":"Performance", "event_type_id":"15", "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.", "occurrence_notes":null, "guid":"125711-21855657@events.umich.edu", "permalink":"http:\/\/events.umich.edu\/event\/125711", "building_id":"1000394", "building_name":"Lurie Ann & Robert H. Tower", "campus_maps_id":"91", "room":"", "location_name":"Lurie Ann & Robert H. Tower", "has_livestream":0, "cost":"Free - no tickets required", "tags":["Faculty","Free","Music","North Campus","Talk"], "website":"", "sponsors":[ { "group_name":"School of Music, Theatre & Dance (SMTD)", "group_id":"155", "website":"http:\/\/smtd.umich.edu\/events" } ], "image_url":"https:\/\/events.umich.edu\/media\/attachments\/2024\/09\/event_125711_original-1.jpg", "styled_images":{ "event_thumb":"https:\/\/events.umich.edu\/media\/cache\/event_thumb\/media\/attachments\/2024\/09\/event_125711_original-1.jpg", "event_large":"https:\/\/events.umich.edu\/media\/cache\/event_large\/media\/attachments\/2024\/09\/event_125711_original-1.jpg", "event_large_2x":"https:\/\/events.umich.edu\/media\/cache\/event_large_2x\/media\/attachments\/2024\/09\/event_125711_original-1.jpg", "event_large_lightbox":"https:\/\/events.umich.edu\/media\/cache\/event_large_lightbox\/media\/attachments\/2024\/09\/event_125711_original-1.jpg", "group_thumb":"https:\/\/events.umich.edu\/media\/cache\/group_thumb\/media\/attachments\/2024\/09\/event_125711_original-1.jpg", "group_thumb_square":"https:\/\/events.umich.edu\/media\/cache\/group_thumb_square\/media\/attachments\/2024\/09\/event_125711_original-1.jpg", "group_large":"https:\/\/events.umich.edu\/media\/cache\/group_large\/media\/attachments\/2024\/09\/event_125711_original-1.jpg", "group_large_lightbox":"https:\/\/events.umich.edu\/media\/cache\/group_large_lightbox\/media\/attachments\/2024\/09\/event_125711_original-1.jpg", "event_large_crop":"https:\/\/events.umich.edu\/media\/cache\/event_large_crop\/media\/attachments\/2024\/09\/event_125711_original-1.jpg", "event_list":"https:\/\/events.umich.edu\/media\/cache\/event_list\/media\/attachments\/2024\/09\/event_125711_original-1.jpg", "event_list_2x":"https:\/\/events.umich.edu\/media\/cache\/event_list_2x\/media\/attachments\/2024\/09\/event_125711_original-1.jpg", "event_grid":"https:\/\/events.umich.edu\/media\/cache\/event_grid\/media\/attachments\/2024\/09\/event_125711_original-1.jpg", "event_grid_2x":"https:\/\/events.umich.edu\/media\/cache\/event_grid_2x\/media\/attachments\/2024\/09\/event_125711_original-1.jpg", "event_feature_large":"https:\/\/events.umich.edu\/media\/cache\/event_feature_large\/media\/attachments\/2024\/09\/event_125711_original-1.jpg", "event_feature_thumb":"https:\/\/events.umich.edu\/media\/cache\/event_feature_thumb\/media\/attachments\/2024\/09\/event_125711_original-1.jpg" }, "occurrence_count":1, "first_occurrence":21855657 } }