Abstract
Like dismantling for finite posets, a perfect sequence Π = 〈P ξ :ξ≤λ〉 of a chain complete posetP represents a canonical procedure to produce a coreP λ. It has been proved that if the posetP contains no infinite antichain then this coreP λ is a retract ofP andP has the fixed point property iffP λ has this property. In this paper the condition of having no infinite antichain is replaced by a weaker one. We show that the same conclusion holds under the assumption thatP does not contain a one-way infinite fence or a tower.
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Communicated by E. C. Milner
Supported by a grant from The National Natural Science Foundation of China.
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Li, B. The core of a chain complete poset with no one-way infinite fence and no tower. Order 10, 349–361 (1993). https://doi.org/10.1007/BF01108829
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DOI: https://doi.org/10.1007/BF01108829