[FOM] Categoricity in f.o.m./2

[Harvey Friedman]

Continuation of http://www.cs.nyu.edu/pipermail/fom/2016-April/019643.html

We give a categoricity theorem for set theory using class theory for
the meta theory, that much more directly addresses
https://golem.ph.utexas.edu/category/2016/03/foundations_of_mathematics.html
than what I wrote in
http://www.cs.nyu.edu/pipermail/fom/2016-April/019643.html

Incidentally, the model M I discussed in
http://www.cs.nyu.edu/pipermail/fom/2016-April/019643.html is not
correctly identified in
http://www.cs.nyu.edu/pipermail/fom/2016-April/019649.html The model M
I discussed is the least (V(lambda),epsilon) satisfying ZFC.

DEFINITION. (in class theory). A model is a pair (D,R), where D is a
nonempty class and R is a binary relation on D. (D,R) is set
respecting if and only if the classes {y: y R x}, x in D, comprise the
subSETS of D.

THEOREM. There is exactly one set respecting model of Extensionality +
Foundation, up to isomorphism. It is (V,epsilon). This is provable in
NBG + AxC.

Harvey Friedman