[FOM] Hilbert's Vollstandigkeitsaxiom and Hilbert's Hotel

Erich Reck erich.reck at ucr.edu
Sun Jan 28 23:22:39 EST 2007

Concerning Andrei Rodin's questions about Hilbert:

Several of the questions raised (especially: Can Hilbert's intuition  
concerning the existence of maximal models of mathematical theories  
be justified? Was it plainly wrong? How "completeness" in Hilbert's  
sense relates to semantic completeness? How it relates to  
categoricity? (Hilbert's completeness implies categoricity but not  
the other way round.) Can one say more?) are addressed, in some  
detail, in "Completeness and Categoricity, Part I: Nineteenth-Century  
Axiomatics to Twentieth-Century Metalogic", S. Awodey & E. Reck,  
History and Philosophy of Logic 23:1, 2002, pp. 1-30.  Compare also  
the second part of that essay, in HPL 23:2, 2002, pp. 77-94, which  
continues the story into the twenty-first century.  (I have referred  
to this paper before, but thought it might be helpful to do so again  
in this context.)

Erich Reck

Erich Reck (Assoc. Prof.), Dept. of Philosophy
University of California, Riverside, CA 92521
Phone: (951) 827-7288; Fax: (951) 827-5298
Webpage: http://www.faculty.ucr.edu/~reck/

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