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There are no infinite order polynomially complete lattices, after all

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Abstract.

If L is a lattice with the interpolation property whose cardinality is a strong limit cardinal of uncountable cofinality, then some finite power \(L^n\) has an antichain of size \(\kappa\). Hence there are no infinite opc lattices. However, the existence of strongly amorphous sets implies (in ZF) the existence of infinite opc lattices.

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Authors and Affiliations

  1. Institut für Algebra, Technische Universitä Wien, Wiedner Hauptstrasse 8-10/118.2, A-1040 Wien, Austria, e-mail: Martin.Goldstern@tuwien.ac.at URL: http://info.tuwien.ac.at/goldstern/ , , , , , , AT

    M. Goldstern

  2. Department of Mathematics, Hebrew University of Jerusalem, Givat Ram, 91904 Jerusalem, Israel, e-mail: shelah@math.huji.ac.il, URL: http://math.rutgers.edu/shelah/, , , , , , IL

    S. Shelah

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  1. M. Goldstern
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  2. S. Shelah
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Received November 2, 1998; accepted in final form March 19, 1999.

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Goldstern, M., Shelah, S. There are no infinite order polynomially complete lattices, after all. Algebra univers. 42, 49–57 (1999). https://doi.org/10.1007/s000120050122

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  • DOI: https://doi.org/10.1007/s000120050122

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