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I'm thinking about buying . Both books are getting excellent reviews at Amazon, especially Goldrei.
I would like to learn about the ZFC axioms, cardinals and ordinals, etc. I assume both books will cover those topics. I'm also very curious about something I heard for the first time today:
Am I reading this right? Every set in ZFC theory can be constructed from the empty set by iterating the power set operation?! That sounds weird. I know you can define the integers this way, and infinite ordinals I guess, but everything else?
0={}
1={0}
2={0,1}
...
If this one axiom leads to all the ZFC axioms, then I should have heard about this before, so I feel that I must have misunderstood something.
Do both of these books explain these things?
I would like to learn about the ZFC axioms, cardinals and ordinals, etc. I assume both books will cover those topics. I'm also very curious about something I heard for the first time today:
Wikipedia (the page about Russell's paradox) said:...the structure of what some see as the "natural" objects described by ZFC eventually became clear; they are the elements of the von Neumann universe, V, built up from the empty set by transfinitely iterating the power set operation.
Am I reading this right? Every set in ZFC theory can be constructed from the empty set by iterating the power set operation?! That sounds weird. I know you can define the integers this way, and infinite ordinals I guess, but everything else?
0={}
1={0}
2={0,1}
...
If this one axiom leads to all the ZFC axioms, then I should have heard about this before, so I feel that I must have misunderstood something.
Do both of these books explain these things?
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