There are no infinite order polynomially complete lattices, after all

M. Goldstern; S. Shelah

doi:10.1007/s000120050122

There are no infinite order polynomially complete lattices, after all

M. Goldstern^*, S. Shelah

^*Corresponding author for this work

Einstein Institute of Mathematics

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

Abstract

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

Original language	English
Pages (from-to)	49-57
Number of pages	9
Journal	Algebra Universalis
Volume	42
Issue number	1-2
DOIs	https://doi.org/10.1007/s000120050122
State	Published - 1999

Keywords

Amorphous set
Axiom of choice
Inaccessible cardinal
Interpolation property
Lattice
Polynomially complete

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10.1007/s000120050122

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

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KW - Axiom of choice

KW - Inaccessible cardinal

KW - Interpolation property

KW - Lattice

KW - Polynomially complete

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There are no infinite order polynomially complete lattices, after all

Abstract

Keywords

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