Books on Axioms: ZF(C) & Why It's Complete

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The discussion focuses on finding books about axioms, particularly ZF(C) and its completeness. Participants clarify that ZF(C) is known to be incomplete due to Gödel's theorem, but they explore different definitions of completeness in axiomatic systems. Recommended readings include "Introduction to Set Theory" by Hrbacek and Jech, and the more advanced "Set Theory" by Jech. Additionally, Van den Dries' lecture notes are highlighted as a valuable resource on consistency and provability. The conversation emphasizes the nuances of completeness in axiomatic frameworks.
Pi3.1415
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Does anyone know of any good books on Axioms. Such as how was ZF(C) came up with and why it is that the general consensus is that it is complete.
 
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Pi3.1415 said:
why it is that the general consensus is that it is complete.
It's well known that ZFC is incomplete, by Gödel's theorem. Or do you mean something else by complete?
 
Oh i see what you mean. I think another definition of completeness in Axiom systems is that no new axioms can be added that will make the new system inconsistent.
 
The book "Introduction to set theory" by Hrbacek and Jech is a good one.
A more advanced book is "Set theory" by Jech.
 
Pi3.1415 said:
Oh i see what you mean. I think another definition of completeness in Axiom systems is that no new axioms can be added that will make the new system inconsistent.
That's the same meaning of completeness I just referred to...
 
Pi3.1415 said:
Oh i see what you mean. I think another definition of completeness in Axiom systems is that no new axioms can be added that will make the new system inconsistent.

Surely you mean "no new axioms can be added that will not make the new system inconsistent".
 
yep sorry now you see why i need the books...
 
Thank you micromass :)
 

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