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On 8/16/2024 5:03 PM, Richard Damon wrote:That is not sufficient. They also had to Comprehension.On 8/16/24 5:35 PM, olcott wrote:On 8/16/2024 4:05 PM, Richard Damon wrote:On 8/16/24 4:39 PM, olcott wrote:On 8/16/2024 2:42 PM, Richard Damon wrote:On 8/16/24 2:11 PM, olcott wrote:On 8/16/2024 11:32 AM, Richard Damon wrote:On 8/16/24 7:02 AM, olcott wrote:No, they defined not only what WAS a set, but what you could do as basic operations ON a set.None of this is changing any more rules. AllI guess you haven't read the papers of Zermelo and Fraenkel. They created a new definition of what a set was, and then showed what that implies, since by changing the definitions, all the old work of set theory has to be thrown out, and then we see what can be established.ZFC didn't need to do that. All they had to do isIf you want to do that, you need to start at the basics are totally reformulate logic.Not at all. I am doing the same sort thing that ZFC*This abolishes the notion of undecidability*But you clearly don't understand the meaning of "undecidability"
As with all math and logic we have expressions of language
that are true on the basis of their meaning expressed
in this same language. Unless expression x has a connection
(through a sequence of true preserving operations) in system
F to its semantic meanings expressed in language L of F
x is simply untrue in F.
did to conquer Russell's Paradox.
redefine the notion of a set so that it was no longer
incoherent.
of these are the effects of the change of the
definition of a set.
Axiom of extensibility: the definition of sets being equal, that ZFC is built on first-order logic.Axion of regularity/Foundation: This is the rule that a set can not be a member of itself, and that we can count the members of a set.This one is the key that conquered Russell's Paradox.
If anything else changed it changed on the basis of this change
or was not required to defeat RP.
This is added to keep most of Comprenesion but not Russell's set.Axiom Schema of Specification: We can build a sub-set from another set and a set of conditions. (Which implies the existance of the empty set)
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