A chain complete poset with no infinite antichain has a finite core |
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Authors: | Boyu Li E. C. Milner |
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Affiliation: | (1) Northwestern University, Xi'an, Shaanxi, P.R. of China;(2) Department of Mathematics, University of Calgary, T2N 1N4, Alberta, Canada |
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Abstract: | It is well known that dismantling a finite posetP leads to a retract, called the core ofP, which has the fixed-point property if and only ifP itself has this property. The PT-order, or passing through order, of a posetP is the quasi order defined onP so thatab holds if and only if every maximal chain ofP which passes througha also passes throughb. This leads to a generalization of the dismantling procedure which works for arbitrary chain complete posets which have no infinite antichain. We prove that such a poset also has a finite core, i.e. a finite retract which reflects the fixed-point property forP.This research was written while the first author was visiting the University of Calgary.Research supported by NSERC grant #69-0982. |
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Keywords: | 06A06 |
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