deletions | additions       diff --git a/appendix_section_Irrational_individuals_Theoretically__.tex b/appendix_section_Irrational_individuals_Theoretically__.tex  index 9e02b65..3aae0ae 100644  --- a/appendix_section_Irrational_individuals_Theoretically__.tex  +++ b/appendix_section_Irrational_individuals_Theoretically__.tex 
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A model is stable if and only if the formula $p \leftrightarrow\Box p$ is a validity. That is to say $p$ is a fixpoint of $\Box p$.   - Since $\Box p$ is a positive formula (and hence $\Box$ denotes a monotonic function from sets of states to sets of states) the Knaster-Tarski fixpoint theorem applies: so we know that a smallest and largest fixpoints exist (and possibly more in-between). The smallest fixpoint is the empty-set (nothing is $p$) and the largest is the whole domain (everything is $p$).   \section{Convergence}  \section{convergence}  NOTE FOR LATER: WE CAN GIVE THE PARALLEL RESULTS FOR THE CASE OF THE UNANIMITY RULE ON (NON-NECESSARILY-FUNCTIONAL) SYMMETRIC INFLUENCE GRAPHS. WE CAN GIVE THE CLASS OF INFLUENCE PROFILES WHICH GUARANTEE CONVERGENCE OF ALL OPINIONS PROFILES, AND WE CAN GIVE THE CLASS OF OPINION PROFILES WHICH CONVERGE ON THE OTHER INFLUENCE PROFILES:   \begin{proposition}  Let $\G=(G_{p_1},\dots,G_{p_m})$ be a SYMMETRIC AND NON-NECESSARILY FUNCTIONAL influence profile and $\O=(O_1,\dots,O_n)$ be an opinion profile.