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  • 1 Department of Mathematics, Morgan State University, 1700 E. Cold Spring Lane, Baltimore, MD 21251, United States of America
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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.

  • [1]

    Birkhoff, G. Lattice Theory (third edition). American Mathematical Society, Providence, Rhode Island, 1967.

  • [2]

    Davey, B. A., and Priestley, H. A. Introduction to Lattices and Order (second edition). Cambridge University Press, Cambridge, 2002.

  • [3]

    Farley, J. D. Cancel Culture: The Search for Universally Cancellable Exponents ofPosets. Manuscript (2021).

  • [4]

    Proctor, R. A., and Scoppetta, L. M. d-complete Posets: Local Structural Axioms, Properties, and Equivalent Definitions. Order 36 (2019), 399-422.

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