Thematics Of Order

[Antti Karttunen]

Jon Awbrey wrote:

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>TOO.  Note 1
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>Propositional logic exemplifies the following property:
>The set of propositions forms a partially ordered set
>under the implication relation [=>], and propositions
>'about' the order are propositions 'in' the order.
>Specifically, a proposition of the form X => Y,
>which says that X is less than or equal to Y
>in the associated partial order, is itself
>an element of the partially ordered set.
>
>This property of "reflective order closure" (ROC)
>has some interesting generalizations in the realm
>of number theory that I would like to exposit here.
>Peirce Listers may consider this line of inquiry as
>incidentally relevant to Peirce's reflections on the
>possible closure of the intentional orders of terms.
>SeqFan Denizens may regard this as a permutational
>perspective on the properties of A000027, formerly
>known as M0472 and N0173.
>
>Cf: http://www.research.att.com/projects/OEIS?Anum=A000027
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Dear Jon,

Please give us an example, how do you induce/produce permutations of
the Natural numbers this way, or tell us whether there are already 
illustrative
specimens in the OEIS. (It is then much easier for my concrete mind to
grasp the concept...)

Thanks,

Antti Karttunen


>Jon Awbrey
>
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>inquiry e-lab: http://stderr.org/pipermail/inquiry/
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