3 problems

Finite-level non-structure conjecture. The theory $T$ has $2^\kappa$ models of cardinality $\mu$ that are pairwise non-isomorphic over $P$.

Higher instability conjecture. The theory $T$ has $2^\lambda$ models of cardinality $\mu$ that are pairwise non-isomorphic over $P$.

Generalized Gaifman conjecture. The theory $T$ has $2^\lambda$ models of cardinality $\mu$ that are pairwise non-isomorphic over $P$.