  These informal definitions need to be tightened up in a rigorous development, but their meaning should be clear to the reader. Now the usual notions of truth, validity, satisfiability, and model for formulas and sentences of  L(κ,λ)  become available. In particular, if A is an  L-structure  and σ ∈ Sent(κ,λ), we shall write A  ⊨ σ  for A is a model of σ, and  ⊨  σ for σ is valid, that is, for all A, A  ⊨ σ.  If Δ ⊆ Sent(κ,λ), we shall write Δ  ⊨  σ for σ is a logical consequence of Δ, that is, each model of Δ is a model of σ.