Natural Partial Orders
1968 ◽
Vol 20
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pp. 535-554
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Let n be an ordinal. A partial ordering P of the ordinals T = T(n) = {w: w < n} is called natural if x P y implies x ⩽ y.A natural partial ordering, hereafter abbreviated NPO, of T(n) is thus a coarsening of the natural total ordering of the ordinals. Every partial ordering of a finite set 5 is isomorphic to a natural partial ordering. This is a consequence of the theorem of Szpielrajn (5) which states that every partial ordering of a set may be refined to a total ordering. In this paper we consider only natural partial orderings. In the first section we obtain theorems about the lattice of all NPO's of T(n).
2009 ◽
Vol 21
(11)
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pp. 3228-3269
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2002 ◽
Vol 16
(1)
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pp. 129-137
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1998 ◽
Vol 35
(1)
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pp. 221-228
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1992 ◽
Vol 24
(03)
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pp. 604-634
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1996 ◽
Vol 119
(4)
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pp. 631-643
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1949 ◽
Vol 1
(2)
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pp. 176-186
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