BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Keita Yokoyama (Japan Advanced Institute of Science and Technology ) DTSTART:20201216T003000Z DTEND:20201216T013000Z DTSTAMP:20260423T005732Z UID:CTA/37 DESCRIPTION:Title: Aut omorphism argument and reverse mathematics\nby Keita Yokoyama (Japan A dvanced Institute of Science and Technology) as part of Computability theo ry and applications\n\n\nAbstract\nIn the study of models of Peano (or fir st-order) arithmetic\, there are\nmany results on recursively saturated mo dels and their automorphisms.\nHere\, we apply such an argument to models of second-order arithmetic\nand see that any countable recursively saturat ed model (M\,S) of WKL_0*\nis isomorphic to its countable coded omega-subm odel if\nSigma_1-induction fails in (M\,S). From this result\, we see some \ninteresting but weird properties of WKL_0* with the absence of\nSigma_1- induction such as the collapse of analytic hierarchy. This\nargument can a lso be applied to the reverse mathematical study of\nRamsey's theorem for pairs (RT22)\, and we see some new relations\nbetween the computability-th eoretic characterizations of RT22 and the\nfamous open question on the fir st-order part of RT22+RCA_0.\nThis work is a part of a larger project join t with Marta Fiori\nCarones\, Leszek Kolodziejczyk\, Katarzyna Kowalik and Tin Lok Wong.\n LOCATION:https://researchseminars.org/talk/CTA/37/ END:VEVENT END:VCALENDAR