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A THEORY OF STRONG INDISCERNIBLES
by
Harvey M. Friedman
April 28, 1999
The Complete Theory of Everything (CTE) is based on certain
axioms of indiscernibility. Such axioms of indiscernibility
have been given a philosophical justification by Kit Fine. I
want to report on an attempt to give strong indiscernibility
axioms which might also be subject to such philosophical
analysis, and which prove the consistency of set theory;
i.e., ZFC or more. In this way, we might obtain a (new kind
of) philosophical consistency proof for mathematics.
We start with the usual impredicative theory of types with
infinity, but not extensionality, and without equality. We
call this ITT. We use infinitely many types (sorts). Objects
of type 1 are the individuals. Objects of type k+1 are the
unary predicates on objects of type k. We use the binary
relation between objects of type k+1 and objects of type k;
namely, the former holds of the latter.
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 Fall '08
 JOSHUA
 Math, Firstorder logic, free variable xk

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