The theory is not categorical in any infinite cardinal. In cardinality $\aleph_0$, one may add no infinite equivalence class or one countably infinite class; these models are not isomorphic. For uncountable $\kappa$, one can vary the number and cardinalities of infinite classes while retaining infinitely many classes of every finite size. These choices are isomorphism invariants.


Solution

Past exam of the mathematics course of the University of Cambridge / 2026 / iii / Paper 144 / 1 / b / Solution

 Solution (source code)