Re: Axiom of Pairing, Scheme of Replacement from others



On Thu, 18 Jan 2007 10:59:28 -0500, "Stephen J. Herschkorn"
<sjherschko@xxxxxxxxxxxx> wrote:


Is it possible to derive the Axiom of Pairing and the Scheme of
Replacement from the Axioms of Extensionality, Union, Power, and
Infinity and the Scheme of Comprehension? How?

No.

Note that Fraenkel added Replacement (as an axiom schema) to the
axioms original proposed by Zermelo. (->ZFC)


F.

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.



Relevant Pages

  • Re: ZFC in another shape.
    ... the strong version of replacement. ... Actually there is no need to prove union. ... You see we can define Successor from the axiom of ordinal succession. ... Now we can proceed to define infinity: ...
    (sci.math)
  • Re: Scheme of Replacement: two versions
    ... From another recent thread ("Axiom of Pairing, Scheme of Replacement ... Fraenkel himself already mentions two different formulations (in Paul ...
    (sci.math)
  • Re: ZFC in another shape.
    ... the strong version of replacement. ... Actually there is no need to prove union. ... You see we can define Successor from the axiom of ordinal succession. ... Now we can proceed to define infinity: ...
    (sci.math)
  • Re: Godel proved maths inconsistent not incompleteness theorem
    ... replacement and the power set axiom. ... There are different versions of the axiom schema of replacement in the ...
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  • Re: Axiom of Pairing, Scheme of Replacement from others
    ... separation follows from the axiom of replacement together with the axiom ... empty set is required. ...
    (sci.math)

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