A Delta(0) (2)-poset with no positive presentation

作者：Wallbaum J^*

来源：Algebra and Logic, 2012, 51(4): 281-284.

DOI：10.1007/s10469-012-9191-8

• partially ordered set
• local lattice
• computably enumerable set

S. Yu. Podzorov in [Mat. Trudy, 9, No. 2, 109-132 (2006)] proved the following theorem. Let aOE (c) L, a parts per thousand currency sign (L) > be a local lattice and v a numbering of L such that the relation v(x) a parts per thousand currency sign (L) v(y) is Delta(0) (2)-computable. Then there is a numbering mu of L such that the relation mu(x) a parts per thousand currency sign (L) mu(y) is computably enumerable. Podzorov also asked whether the hypothesis that aOE (c) L, a parts per thousand currency sign (L) > is a local lattice is needed or the theorem is true of any partially ordered set (poset). We answer his question by constructing a poset for which the conclusion of the theorem fails.

• 出版日期2012-9