关于d-完全序集的Proctor和Scoppetta猜想的证明

Mathematica Pannonica Pub Date : 2022-03-09 DOI:10.1556/314.2022.00009

J. Farley

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摘要

Proctor和Scoppetta推测(1)存在一个无限局部有限偏序集满足他们的条件VT和NTC而不满足SIS;(2)存在一个无限的局部有限偏序集满足它们的条件D3-C和D3MF，但不同时满足VT和FT;(3)存在一个无限的局部有限偏序集满足它们的条件D3-C和D3MD，但不满足NCC。本文证明了与d-完全偏序集有关的Proctor和Scoppetta猜想。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Proof of a Conjecture of Proctor and Scoppetta Related to d-Complete Posets

Proctor and Scoppetta conjectured that (1) there exists an infinite locally finite poset that satisfies their conditions VT and NTC but not SIS; (2) there exists an infinite locally finite poset satisfying their conditions D3-C and D3MF but not both VT and FT; and (3) there exists an infinite locally finite poset satisfying their conditions D3-C and D3MD but not NCC. In this note, the conjecture of Proctor and Scoppetta, which is related to d-complete posets, is proven.

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Mathematica Pannonica

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