Date: Apr 4, 2013 5:47 PM
Author: fom
Subject: Re: Matheology § 224

On 4/4/2013 4:10 PM, Virgil wrote:
> In article
> <f1f264eb-e018-4e90-98c1-abffa261e23c@gp5g2000vbb.googlegroups.com>,
> WM <mueckenh@rz.fh-augsburg.de> wrote:
>

>>> No, a collection is no more and no less than "all its elements".
>>
>> But an inductive set contains elements that are not subject to
>> induction?

>
> Only in Wolkenmuekenheim!
>


Check the definitions.

The intersection of the class of all inductive sets
containing the empty set is the inductive set for
which every element has a finite chain of predecessors
initiated with the empty set.

But, unlike WM, you are working from your stated definition
which corresponds with a statement of the Dedekind-Peano
axioms. I let myself get confused by all of this switching
back and forth between "obvious" unstated theories.