BEGIN:VCALENDAR VERSION:2.0 PRODID:ILLC Website X-WR-TIMEZONE:Europe/Amsterdam BEGIN:VTIMEZONE TZID:Europe/Amsterdam X-LIC-LOCATION:Europe/Amsterdam BEGIN:DAYLIGHT TZOFFSETFROM:+0100 TZOFFSETTO:+0200 TZNAME:CEST DTSTART:19700329T020000 RRULE:FREQ=YEARLY;BYMONTH=3;BYDAY=-1SU END:DAYLIGHT BEGIN:STANDARD TZOFFSETFROM:+0200 TZOFFSETTO:+0100 TZNAME:CET DTSTART:19701025T030000 RRULE:FREQ=YEARLY;BYMONTH=10;BYDAY=-1SU END:STANDARD END:VTIMEZONE BEGIN:VEVENT UID:/NewsandEvents/Archives/2015/newsitem/6804/27- March-2015-Cool-Logic-Michal-Tomasz-Godziszewski DTSTAMP:20150322T000000 SUMMARY:Cool Logic, Michal Tomasz Godziszewski ATTENDEE;ROLE=Speaker:Michal Tomasz Godziszewski DTSTART;TZID=Europe/Amsterdam:20150327T173000 DTEND;TZID=Europe/Amsterdam:20150327T183000 LOCATION:F1.15 ILLC seminar room, Science Park 107 , Amsterdam DESCRIPTION:We consider the properties of the arit hmetically simplest class of universal (i.e. $\\Pi ^0_1$) sentences undecidable in sufficiently stron g arithmetical theories. Following the framework o f experimental logic and results of R. G. Jeroslow obtained in Jer75, we therefore answer an epistem ological question about cognitive reasons of epist emic hardness of undecidable arithmetical sentence s. We prove that by adjoining the minimal (in the sense of being on a very low level of arithmetical hierarchy) possible set of undecidable sentences to recursive set of axioms of arithmetical theory and closing it under logical consequence, we obtai n a theory such that it is not algorithmically lea rnable (i.e. not $\\Delta^0_2$). For more inform ation, see http://www.illc.uva.nl/coollogic/ or co ntact coollogic.uva at gmail.com X-ALT-DESC;FMTTYPE=text/html:\n
We consi der the properties of the arithmetically simplest class of universal (i.e. $\\Pi^0_1$) sentences und ecidable in sufficiently strong arithmetical theor ies. Following the framework of experimental logic and results of R. G. Jeroslow obtained in Jer75, we therefore answer an epistemological question ab out cognitive reasons of epistemic hardness of und ecidable arithmetical sentences. We prove that by adjoining the minimal (in the sense of being on a very low level of arithmetical hierarchy) possible set of undecidable sentences to recursive set of axioms of arithmetical theory and closing it under logical consequence, we obtain a theory such that it is not algorithmically learnable (i.e. not $\\ Delta^0_2$).
\n \nFor more infor mation, see http://www.illc.uva.nl/cooll ogic/ or contact coollogic.uv a at gmail.com
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