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1
SENTENTIAL REFLECTION
by
Harvey M. Friedman
Ohio State University
Princeton University
friedman@math.ohiostate.edu
http://www.math.ohiostate.edu/~friedman/
January 5, 2003
Abstract. We present two forms of “sentential reflection”,
which are shown to be mutually interpretable with Z
2
and
ZFC, respectively.
1. Introduction.
We use “class” as a neutral term, without commitment to the
developed notions of “set” and “class” that have become
standard in set theory and mathematical logic. We use for
membership.
This framework supports interpretations of sentential
reflection that may differ from conventional set theory or
class theory. However, we do not pursue this direction
here.
This framework is intended to accommodate objects that are
not classes. Such nonclasses are treated as classes with no
elements. Thus we are careful not to assume extensionality.
In fact, we will not assume any form of extensionality.
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 Fall '08
 JOSHUA
 Math

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