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Antonio Speltzu

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Mar 9, 2022, 6:14:39 PM3/9/22
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Let L be a numerable language and M be a model of LN in which every recursive unary relation is expressible. M cannot be recursive in a numbering of L in which L1 is recursive.

Antonio Speltzu

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Mar 10, 2022, 3:25:49 AM3/10/22
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El jueves, 10 de marzo de 2022 a las 0:14:39 UTC+1, Antonio Speltzu escribió:
> Let L be a numerable language and M be a model of LN in which every recursive unary relation is expressible. M cannot be recursive in a numbering of L in which L1 is recursive.

Subtle theorem where there are.

Rupert

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Mar 10, 2022, 3:52:33 AM3/10/22
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On Thursday, March 10, 2022 at 12:14:39 AM UTC+1, Antonio Speltzu wrote:
> Let L be a numerable language and M be a model of LN in which every recursive unary relation is expressible. M cannot be recursive in a numbering of L in which L1 is recursive.

"numerable language" - meaning what? set of symbols is countable?

"LN" - meaning of this notation?

It's not possible to make any sense of this.

Antonio Speltzu

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Mar 10, 2022, 11:34:19 AM3/10/22
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https://www.academia.edu/73390840/L%C3%B3gica_Matem%C3%A1tica

Antonio Speltzu

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Mar 11, 2022, 12:27:11 PM3/11/22
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Example: The model associated with the free language generated by recursive unary relations.

Ross A. Finlayson

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Mar 11, 2022, 7:51:00 PM3/11/22
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It seems pretty usual, why is this different than a usual statement of
"incompleteness of 2'nd order arithmetic"?

Ross A. Finlayson

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Mar 11, 2022, 7:52:32 PM3/11/22
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(Figuring that Louwenheim/Skolem theorems up and down are also usual.)

Antonio Speltzu

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Mar 12, 2022, 3:32:54 PM3/12/22
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El jueves, 10 de marzo de 2022 a las 0:14:39 UTC+1, Antonio Speltzu escribió:
> Let L be a numerable language and M be a model of LN in which every recursive unary relation is expressible. M cannot be recursive in a numbering of L in which L1 is recursive.

Better, M is not recursive at for any numbering of L.

Julio Di Egidio

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Mar 12, 2022, 3:41:57 PM3/12/22
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And same goes here: why don't you too just stop feeding the trolls??

You guys really have nothing better to do than shit all over the place, do you?

Epically pathetic and ultimately stupid... I hope you all manage to get yourself
extinct as soon as possible.

*Plonk*

Julio

Ross A. Finlayson

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Mar 13, 2022, 4:37:59 AM3/13/22
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Most people never read Cohen's papers on Independence of CH,
which we've discussed here and you can read at your leisure.

Antonio Speltzu

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Mar 16, 2022, 12:09:09 PM3/16/22
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Summarizing:
If L is a countable language and M a model of LN in which
every recursive set is definable, then M is not recursive.
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