Abstract
We introduce semilattices equipped with a partial n-ary operation ρ. A useful separation lemma for such nontrivial complete partial ρ-semilattices is proved equivalent to PIT, the prime ideal theorem. The relation of various versions of the Lemma to each other and to PIT is also explored.
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Supported by the Ministry of Education of the Czech Republic under the project MSM0021622409.
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Paseka, J. More on the Strength of Engeler’s Lemma. Order 25, 69–77 (2008). https://doi.org/10.1007/s11083-008-9078-4
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DOI: https://doi.org/10.1007/s11083-008-9078-4