Decision Methods in the Theory of Ordinals
For an ordinal α, let RS(α), the restricted second order theory of [α, <], be the interpreted formalism containing the first order theory of [α, <] and quantification on monadic predicate variables, ranging over all subsets of α. For a cardinal γ, RS(α, γ) is like RS(α), except that the predicate variables are now restricted to range over subsets of α of cardinality less than γ. ω = ω 0 and ω 1 denote the first two infinite cardinals. In this note I will outline results concerning RS(α, ω 0), which were obtained in the Spring of 1964 (detailed proofs will appear in ), and the corresponding stronger results about RS(α, ω 1), which were obtained in the Fall of 1964.
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