Measures, states and de Finetti maps on pseudo-BCK algebras
In this paper we extend the notions of states and measures presented in Dvurecenskij and Pulmannova (2000) [12] to the case of pseudo BCK algebras and study similar properties We prove that under some conditions the notion of a state in the sense of Dvurecenskij and Pulmannova (2000) [12] coincides with the Bosbach state and we extend to the case of pseudo BCK algebras some results proved by Kuhr only for pseudo BCK semilattices We characterize extremal states, and show that the quotient pseudo BCK algebra over the kernel of a measure can be embedded into the negative cone of an archimedean l group Additionally we introduce a Borel state and using results by Kuhr and Mundici (2007) [28], we prove a relationship between de Finetti maps Bosbach states and Borel states (C) 2010 Elsevier B V All rights reserved
pseudo bck algebra bosbach state extremal state borel state mv algebra state morphism l group