On ordinals accessible by infinitary languages
Saharon Shelah, Pauli Väisänen, Jouko Väänänen (2005)
Fundamenta Mathematicae
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Let λ be an infinite cardinal number. The ordinal number δ(λ) is the least ordinal γ such that if ϕ is any sentence of , with a unary predicate D and a binary predicate ≺, and ϕ has a model ℳ with a well-ordering of type ≥ γ, then ϕ has a model ℳ ’ where is non-well-ordered. One of the interesting properties of this number is that the Hanf number of is exactly . It was proved in [BK71] that if ℵ₀ < λ < κ2λ = κ∙ ; ∙ cf(θ) ≥ λ⁺ and whenever μ < θ; ∙ . Then there...