FOM: A slip comes to light
Adrian-Richard-David Mathias
Adrian-Richard-David.Mathias at helios.univ-reunion.fr
Thu Aug 8 16:48:22 EDT 2002
Hazen's CONJECTURE is a variant of the Axiom H of Cole and Mitchell
studied in my paper "The Strength of Mac Lane Set Theory"
(APAL 110 (2001) pp 110-234).
Axiom H says that for every set u there is a transitive set T
such that every transitive set injectible into u is a subset of T.
Proposition 3.2 of my paper says that over a certain weak base system
which I call M_0, Axiom H is equivalent to the statement
("Mostowski's principle") that every
extensional well-founded relation is isomorphic to a transitive
set.
The forward direction is fine; but reflecting on the context with
a proper class of Quine atoms, I now realise that the short derivation
that I give in the paper, of Axiom H from Mostowski's principle,
implicitly relies on the Axiom of Foundation , which is not among
the axioms of M_0. So my Proposition 3.2 is incorrect as stated.
I *HOPE* that doesn't affect anything later on, but I haven't yet
checked. Fortunately I am assuming Foundation for most of the time.
A. R. D. Mathias
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