Thematics Of Order

[Jon Awbrey]

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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

Jon Awbrey

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inquiry e-lab: http://stderr.org/pipermail/inquiry/
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