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From: Mikko <mikko.levanto@iki.fi>
Newsgroups: sci.logic
Subject: Re: This makes all Analytic(Olcott) truth computable
Date: Mon, 19 Aug 2024 11:54:59 +0300
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On 2024-08-18 12:08:35 +0000, olcott said:

> On 8/18/2024 5:18 AM, Mikko wrote:
>> On 2024-08-16 20:39:11 +0000, olcott said:
>> 
>>> 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:
>>>>>>> 
>>>>>>> *This abolishes the notion 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.
>>>>>> 
>>>>>> But you clearly don't understand the meaning of "undecidability"
>>>>> 
>>>>> Not at all. I am doing the same sort thing that ZFC
>>>>> did to conquer Russell's Paradox.
>>>>> 
>>>>> 
>>>> 
>>>> If you want to do that, you need to start at the basics are totally 
>>>> reformulate logic.
>>>> 
>>> 
>>> ZFC didn't need to do that. All they had to do is
>>> redefine the notion of a set so that it was no longer
>>> incoherent.
>> 
>> As the notion of set is the all what a set theory is about,
>> a redefinition of the notion of a set is means Zermelo started
>> from square one and built an entirely new formal system.
>> 
> 
> The key functional difference was the result of few changes
> and everything else stayed the same. Besides defeating RP
> what was another functional result?

The theory says that the universe of sets is infinite but does
not say whether it is uncountable. Consequently there is a countable
universe that can be proven to contain uncountable sets (and all
their members because the theory says that all memebers are sets).

-- 
Mikko