[FOM] Re: A ... cute? ... axiomatic system

A.P. Hazen a.hazen at philosophy.unimelb.edu.au
Tue Jul 1 03:43:43 EDT 2003

    Update (U/D?) on UDZF.
    I've gotten up my courage to take another look at Church's paper (it's
in "Proceedings of the Tarski Symposium" = vol. 25 of the AMS "Proceedings
of Symposia in Pure Mathematics" series: the big dark red volumes).
    After noticing that  Church included it in his axiomatization, I
thought about my model some more and realized that I could have
strengthened my "finite unions exist" to "every set has a union" (hint:
every red set has the universal set as its union).
    At this  point my axioms-- substituting my "G" for his "wf" (so: "G"
**is** definable)-- include Church's "basic" axioms A through J, plus his
proposed axiom K (every set has a complement).  I haven't worked through
his L-axioms yet, or figured out how close my intuitively described model
is to his formally described one: I repeat my earlier comment about detail
and technicality.
Allen Hazen
Philosophy Department
University of Melbourne

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