FOM: Cardinality Operators

Martin Davis martin at
Thu Jan 27 13:48:09 EST 2000

At 09:27 AM 1/27/00 -0500, Harvey Friedman wrote:
>Digression: Is NBG or VB more historically accurate as a name for this
>class theory? I.e., what exactly was Godel's role?

His monograph on the consistency of GCH used a modification of Bernays' 
modification of von Neumann's axiomatization. The progression was like 
this: Von Neumann had two sorts, sets and mappings; Bernays replaced the 
mappings with classes but retained separate sorts; Goedel merged the two 
sorts defining a set as a member of a class. He took over Bernays' proof of 
comprehension for classes from a finite set of axioms, and of course his 
monograph popularized the system.


                           Martin Davis
                    Visiting Scholar UC Berkeley
                      Professor Emeritus, NYU
                          martin at
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