Re: Axiom of Pairing, Scheme of Replacement from others

Stephen J. Herschkorn wrote:
MoeBlee wrote:

Stephen J. Herschkorn wrote:


Does

(Extensionality, Pairing, Union, Power, Infinity, Comprehension) |-
Replacement?



Which comprehension schema? I take it you don't mean the separation
schema.


Hmm, looking at Halmos, Kunen, and Suppes, it seems to me that
"Comprehension," "Separation," and "Specifcation" (not respectively) all
refer to the same thing:

For any logical formula f wherein the variable "x" is not free, we
have the universal closure of

There exists x such that for all y, y in x iff (y in z and f).

From looking at http://en.wikipedia.org/wiki/Axiom_of_separation , I
suspect maybe MB thought I was referring to unrestricted comprehension.
Does anyone do that any more?

I just wanted to make sure, especially since as taken in the sense of
the axiom scyhema of separation, your question seems to be whether Z |-
ZF, while it is famous that it is not the case that Z |- ZF. Am I
missing something here?

MoeBlee

.

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