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maximal set theory

Consider a class of set theories resembling that of Zermelo except
that we may vary the comprehension axiom.

Naive set theory forms terms {x|wff} for any wff and is inconsistent.
Zermelo set theory allows only {x|xεA ∧ wff1}, i.e. wff is restricted
to have the form  xεA∧wff1.

We consider arbitrary effective classes of allowed wff1, and consider
which of them lead to consistent set theories or at least theories that
can be shown equiconsistent with Zermelo set theory.

Conjecture 1 - There is am effective procedure for getting stronger set theories,
such that if T is a set theory T' = f(T) is stronger but equiconsistent.

Conjecture 2 - If two set theories are consistent, so is their union.  If
this isn't true, we may have to restrict the effective classes we admit
so as to make it true.

Conjecture 3 - The union of all consistent effectively given set theories
is a set theory but is no longer effective.  The idea is that the set of
all intuitively meaningful comprehension terms is not r.e.

Conjecture 4 - Although the above maximal set theory is not r.e., it will
have interesting mathematical properties.

These conjectures are perhaps overbold and should really be called
speculations.