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 thata⊴b 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.
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References
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Communicated by D. Duffus
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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Li, B., Milner, E.C. A chain complete poset with no infinite antichain has a finite core. Order 10, 55–63 (1993). https://doi.org/10.1007/BF01108708
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DOI: https://doi.org/10.1007/BF01108708