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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 https://www.illc.uva.nl/coollogic/ or c
 ontact coollogic.uva at gmail.com
X-ALT-DESC;FMTTYPE=text/html:\n        <p>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 $\\
 Delta^0_2$). </p>\n    \n        <p>For more infor
 mation, see <a target="_blank" href="https://www.i
 llc.uva.nl/coollogic/">https://www.illc.uva.nl/coo
 llogic/</a> or contact <a class="email">coollogic.
 uva <span class="at">at</span> gmail.com</a></p>\n
     
URL:/NewsandEvents/Archives/2015/newsitem/6804/27-
 March-2015-Cool-Logic-Michal-Tomasz-Godziszewski
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