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UID:/NewsandEvents/Archives/2001/newsitem/96/18-De
 cember-2001-Zuidelijk-Interuniversitair-Colloquium
 -ZIC-Dirk-van-Dalen
DTSTAMP:20011207T000000
SUMMARY:Zuidelijk Interuniversitair Colloquium (ZI
 C), Dirk van Dalen
ATTENDEE;ROLE=Speaker:Dirk van Dalen
DTSTART;VALUE=DATE:20011218
DTEND;VALUE=DATE:20011218
LOCATION:Room HG 6.96, TU Eindhoven
DESCRIPTION:In 1918 Brouwer published a principle 
 that was basic for the theory of choice sequences:
  the continuity principle, which says that all map
 pings from choice sequences of natural numbers to 
 natural numbers are continuous. A foundational arg
 ument for the principle was not given. Since then 
 a number of arguments have been put forward to pro
 vide a foundational basis for the principle. None 
 of these have been absolutely successful to the de
 gree that we accept the axioms for arithmetic. We 
 will look into this matter and see what can be don
 e. Also the case of the lawlike sequences is consi
 dered. Furthermore a pedestrian proof of the Kreis
 el-Lacombe-Shoenfield-Tscheitin theorem (all funct
 ions from recursive functionals to natural numbers
  are continuous) will be sketched, using a techniq
 ue, now known as Ishihara's trick.
X-ALT-DESC;FMTTYPE=text/html:\n      <p>In 1918 Br
 ouwer published a principle that was basic for\n  
       the theory of choice sequences: the continui
 ty principle,\n        which says that all mapping
 s from choice sequences of natural\n        number
 s to natural numbers are continuous.  A foundation
 al\n        argument for the principle was not giv
 en.  Since then a number\n        of arguments hav
 e been put forward to provide a foundational\n    
     basis for the principle. None of these have be
 en absolutely\n        successful to the degree th
 at we accept the axioms for\n        arithmetic. W
 e will look into this matter and see what can be\n
         done. Also the case of the lawlike sequenc
 es is considered.\n        Furthermore a pedestria
 n proof of the\n        Kreisel-Lacombe-Shoenfield
 -Tscheitin theorem (all functions\n        from re
 cursive functionals to natural numbers are continu
 ous)\n        will be sketched, using a technique,
  now known as Ishihara's\n        trick.\n      </
 p>\n    
URL:/NewsandEvents/Archives/2001/newsitem/96/18-De
 cember-2001-Zuidelijk-Interuniversitair-Colloquium
 -ZIC-Dirk-van-Dalen
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