Regular Languages and Model Theory 15: Structure-Preserving Maps
In this video, I introduce the concepts of homomorphisms and isomorphisms: functions on structures that "preserve" or "respect" their operations, relations, and constants.
You can find a proof that all first order logical properties preserved under homomorphism can be given by positive formulas in Roger Lyndon's "Properties Preserved Under Homomorphism": https://projecteuclid.org/journals/pa...