Layers of zero probability and stable coherence over źukasiewicz events

AbstractThe notion of stable coherence has been recently introduced to characterize coherent assignments to conditional many-valued events by means of hyperreal-valued states. In a nutshell, an assignment, or book, $$\beta $$β on a finite set of conditional events is stably coherent if there exists a coherent variant $$\beta '$$βź of $$\beta $$β such that $$\beta '$$βź maps all antecedents of conditional events to a strictly positive hyperreal number, and such that $$\beta $$β and $$\beta '$$βź differ by an infinitesimal. In this paper, we provide a characterization of stable coherence in terms of layers of zero probability for books on źukasiewicz logic events.