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arXiv · 1604.08909

When Lexicographic Product of Two po-Groups has the Riesz Decomposition Property

Anatolij Dvurečenskij·Omid Zahiri
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Abstract

We study conditions when a certain type of the Riesz Decomposition Property (RDP for short) holds in the lexicographic product of two po-groups. Defining two important properties of po-groups, we extend known situations showing that the lexicographic product satisfies RDP or even RDP$_1$, a stronger type of RDP. We recall that a very strong type of RDP, RDP$_2$, entails that the group is lattice ordered. RDP's of the lexicographic products are important for the study of lexicographic pseudo effect algebras, or perfect types of pseudo MV-algebras and pseudo effect algebras, where infinitesimal elements play an important role both for algebras as well as for the first order logic of valid but not provable formulas.

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Anatolij Dvurečenskij, Omid Zahiri. 2016-04-29. When Lexicographic Product of Two po-Groups has the Riesz Decomposition Property. https://arxiv.org/abs/1604.08909

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