Abstract
From a constructive point of view, a weak linear order is a negative concept, to be replaced by the positive notion of strict order. It turns out that for a similar positive theory of partial order and lattices, one basic relation is sufficient. The treatment is elementary throughout and uses only free parameters and constructions. In lattice theory, the partial order relation can be characterized through algebraic equalities for lattices. A constructivization of this characterization is given, through use of an apartness relation instead of an equality.
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von Plato, J. (2001). Positive Lattices. In: Schuster, P., Berger, U., Osswald, H. (eds) Reuniting the Antipodes — Constructive and Nonstandard Views of the Continuum. Synthese Library, vol 306. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-9757-9_16
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DOI: https://doi.org/10.1007/978-94-015-9757-9_16
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