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UID:/NewsandEvents/Archives/2022/newsitem/13645/21
 ---22-May-2022-Meeting-in-Internal-Categoricity-He
 lsinki-Finland-Virtual
DTSTAMP:20220515T214231
SUMMARY:Meeting in Internal Categoricity, Helsinki
  (Finland) &  Virtual
DTSTART;VALUE=DATE:20220521
DTEND;VALUE=DATE:20220522
LOCATION:Helsinki (Finland) &  Virtual
DESCRIPTION:The categoricity of an axiom system me
 ans that its non-logical symbols have, up to isomo
 rphism, only one possible interpretation. The firs
 t axiomatizations of mathematical theories such as
  number theory and analysis by Dedekind, Hilbert, 
 Huntington, Peano and Veblen were indeed categoric
 al. These were all second order axiomatisations, s
 uffering from what many consider a weakness, namel
 y dependence on a strong metatheory, casting a sha
 dow over these celebrated categoricity results. In
  finer analysis a new form of categoricity has eme
 rged. It is called internal categoricity because i
 t is perfectly meaningful without any reference to
  a metatheory, and it is now known that the classi
 cal theories, surprisingly even in their first ord
 er formulation, can be shown to be internally cate
 gorical.  In this workshop various aspects of and 
 approaches to internal categoricity are presented 
 and the following questions, among others, are dis
 cussed: What is the philosophical import/advantage
  of internal categoricity over ordinary categorici
 ty? Is internal categoricity the right concept of 
 categoricity? Does internal categoricity play a ro
 le also in first order theories?
X-ALT-DESC;FMTTYPE=text/html:\n  <p>The categorici
 ty of an axiom system means that its non-logical s
 ymbols have, up to isomorphism, only one possible 
 interpretation. The first axiomatizations of mathe
 matical theories such as number theory and analysi
 s by Dedekind, Hilbert, Huntington, Peano and Vebl
 en were indeed categorical. These were all second 
 order axiomatisations, suffering from what many co
 nsider a weakness, namely dependence on a strong m
 etatheory, casting a shadow over these celebrated 
 categoricity results. In finer analysis a new form
  of categoricity has emerged. It is called interna
 l categoricity because it is perfectly meaningful 
 without any reference to a metatheory, and it is n
 ow known that the classical theories, surprisingly
  even in their first order formulation, can be sho
 wn to be internally categorical.</p>\n  <p>In this
  workshop various aspects of and approaches to int
 ernal categoricity are presented and the following
  questions, among others, are discussed: What is t
 he philosophical import/advantage of internal cate
 goricity over ordinary categoricity? Is internal c
 ategoricity the right concept of categoricity? Doe
 s internal categoricity play a role also in first 
 order theories?</p>\n
URL:https://www.helsinki.fi/en/beta/conferences/in
 ternal-categoricity
CONTACT:Juliette Kennedy at juliette.kennedy at he
 lsinki.fi
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