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VERSION:2.0
PRODID:ILLC Website
BEGIN:VEVENT
UID:/NewsandEvents/Events/Upcoming-Events/newsitem
/6804/27-March-2015-Cool-Logic-Michal-Tomasz-Godzi
szewski
DTSTAMP:20150322T000000
SUMMARY:Cool Logic, Michal Tomasz Godziszewski
ATTENDEE;ROLE=Speaker:Michal Tomasz Godziszewski
DTSTART:20150327T173000
DTEND: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 \n For more infor
mation, see http://www.illc.uva.nl/cooll
ogic/ or contact coollogic.uv
a at gmail.com

\n
URL:/NewsandEvents/Events/Upcoming-Events/newsitem
/6804/27-March-2015-Cool-Logic-Michal-Tomasz-Godzi
szewski
END:VEVENT
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