Author:
Jonathan David Farley 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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Editor in Chief: László TÓTH (University of Pécs)

Honorary Editors in Chief:

  • † István GYŐRI (University of Pannonia, Veszprém, Hungary)
  • János PINTZ (Rényi Institute of Mathematics, Budapest, Hungary)
  • Ferenc SCHIPP (Eötvös Loránd University, Budapest, Hungary and University of Pécs, Pécs, Hungary)
  • Sándor SZABÓ (University of Pécs, Pécs, Hungary)
     

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  • István BERKES (Rényi Institute of Mathematics, Budapest, Hungary)
  • Károly BEZDEK (University of Calgary, Calgary, Canada)
  • György DÓSA (University of Pannonia, Veszprém, Hungary)
  • Balázs KIRÁLY – Managing Editor (University of Pécs, Pécs, Hungary)
  • Vedran KRCADINAC (University of Zagreb, Zagreb, Croatia) 
  • Željka MILIN ŠIPUŠ (University of Zagreb, Zagreb, Croatia)
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  • Margit PAP (University of Pécs, Pécs, Hungary)
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  • Mihály PITUK (University of Pannonia, Veszprém, Hungary)
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Mathematica Pannonica
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