[FOM] picture of V
José Ferreirós Domínguez
josef at us.es
Thu Oct 20 04:08:40 EDT 2011
Dear all:
let me ask a very simple question. Who started the tradition of
picturing the set-theoretic universe V with the usual "inverted
cone"? Maybe some of you can make suggestions, perhaps even based on
personal experience?
The idea behind the picture, of course, can be traced back to von
Neumann and Zermelo in the late 1920s (see e.g. Zermelo's paper of
1930, translated in W. Ewald, "From Kant to Hilbert", vol. 2). At the
basis of the famous iterative conception there were sophisticated
technical developments showing that any model of ZFC can be developed
in the form of a cumulative hierarchy. Only afterwards somebody (in
fact, Goedel) proposed the iterative concepcion, the intuitive view
of a step-by-step development of the universe of sets with steps
indexed by the ordinals, the development guided by the powerset
operation. The idea is spelled out in 1947 (What is Cantor's
continuum problem?) and seems to be already clear in his mind in a
lecture of 1933.
But I am curious about the picture itself, which I believe has
special appeal for the individual mathematician learning set theory
and trying to understand what it is about.
Best,
Jose Ferreiros
Departamento de Filosofia y Logica
Universidad de Sevilla
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