[FOM] impredicative definitions/paper announcement

Nik Weaver nweaver at math.wustl.edu
Sat Nov 20 09:10:01 EST 2010

Daniel Mehkeri wrote:

> Kleene's O was mentioned, but it is constructed from below in a
> sense. It is common especially in constructive mathematics to call
> that predicative

Yes, Michael Rathjen calls this kind of thing "generalized predicative".
I would use the term "pseudo-predicative".  Generally you're talking
about constructive reasoning which is genuinely predicative augmented
by one or two axioms which are not (most notably, full set induction).

Incidentally, I have a new survey paper on predicativism (and it does
discuss this point).  It's called "What is predicativism?" and can be
found at


or among my other papers at


Nik Weaver
Math Dept.
Washington University
St. Louis, MO 63130 USA
nweaver at math.wustl.edu

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