On triggers and replication in MySQL I have a classical statement-based replication between the master and the slave. Triggers were created on the master and replicated on the slave as well.

Assuming that I have, say an ON UPDATE trigger, is the following correct? 


  MySQL will only write to the binary log statements that were not the
  result of the trigger. Data consistency between the master and the
  slave is therefore ensured by the fact that the same triggers are
  present on both.


The relevance of this pertains to incremental updates (or accumulutors), eg. 

CREATE TRIGGER vesion_increment AFTER UPDATE ON table
FOR EACH ROW
BEGIN
  UPDATE table SET version=version+1;
END


In this case, the UPDATE table SET version=version+1 will not be in the binary log and hence not replicated but taken care of by the same trigger on the slave. Is that correct?
Yes, you are correct. You can often get bitten from the fact that the triggers are missing on the slave and thus the trigger effects are not there.

Also if the triggers use any routines (PROCEDUREs and FUNCTIONs) you have to make sure they are present on the slave too. The latter might bite you if you provision your slaves from a mysqldump, since by default mysqldump does not dump routines.