Galactic algebra is a clean superset of universal algebra, which suits this intention: to consider semi-functions (partial functions) and subsets of some universe, then to reason in a uniform way about identity (equality of terms), membership, and inclusion. The logic of galactic algebra is expressed as a first-order Hilbert-style system, which has all the desired qualities. — This text means an announcement and a description of my thesis [9]. Only the proof technique is explained.