On 27 Feb 2013, at 13:58, Stephen P. King wrote:

On 2/27/2013 5:18 AM, Bruno Marchal wrote:
[SPK] Are subsets of the UD equivalent to a Boolean Algebra?

The UD is not a set.

Dear Bruno,

   Why are you such a literalist?

Don't use technical terms, in that case.



 Are the strings that make up the UD equivalent to a Boolean algebra?

The UD is one program. It is one string. And UD* is an infinitely complex structure, roughly equivalent to sigma_1 truth, and structured from inside by the 8 hypostases, none being boolean.


Bruno




But doing some effort to translate what you say, the answer is NO. You can make the UD into a set by modeling it by the set of sigma_1 sentences. But the negation of a sigma_1 sentence is not necessarily sigma_1, so it gives not a boolean algebra.


I was only using the word 'subset' to indicate the components of the UD, not a literal subset. Since the UD is not a set, it obviously cannot have subsets, so you should be able to deduce that I am not asking a question that implies otherwise. Let us try again. Are the components of the UD equivalent to Boolean algebras? Yes or No. If not, what relation do they have with boolean algebras?



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Onward!

Stephen


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http://iridia.ulb.ac.be/~marchal/



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