I updated my preprint manuscript Filters on Posets and Generalizations. There are two changes:
1. Added new section “Distributivity of core part over lattice operations”.
2. Removed certain redundant theorem conditions: That a filtrator is with join-close core automatically follows from the fact it is semifiltered. I previously had theorem conditions which were specifying both conditions to be (semi-)filtered and to be join-closed. Now redundant condition to be join-closed is removed from theorem conditions already having “(semi-)filtered” condition.
The updated version of the manuscript is submitted to “Surveys in Mathematics and its Applications” math journal.