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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Computing beyond Constructibility: The Recognizabi
lity Stregth of Ordinal Time Machines - Carl\, M (
Universitt Konstanz)
DTSTART;TZID=Europe/London:20151216T133000
DTEND;TZID=Europe/London:20151216T143000
UID:TALK62917AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/62917
DESCRIPTION:Co-author: Philipp Schlicht (Universitt Bonn)\n\nT
ransfinite machine models of computation provide a
n approach to an `effective mathematics of the unc
ountable'. However\, their set-theoretical interes
t seems to be limited by the fact that even the st
rongest such model\, Koepke's Ordinal Turing Machi
nes with parameters (pOTMs)\, can only compute con
structible sets.\n\nRecognizability is a more libe
ral notion than computability in that it only requ
ires the machine to be able to identify a certain
object when it is given to it as an input\, not to
produce that object.\n\nBy invoking notions from
algorithmic randomness and considering recognizabi
lity rather than computability\, we connect transf
inite computability to large cardinals and forcing
axioms incompatible with the axiom of constructib
ility on the one hand and inner models for large c
ardinals on the other. In particular\, under appro
priate large cardinal assumptions\, a real number
is heriditarily recognizable by a pOTM if and only
if it is an element of the mouse for one Woodin c
ardinal.\nThis is joint work with Philipp Schlicht
.\n
LOCATION:Seminar Room 1\, Newton Institute
CONTACT:
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