Determinacy and Δ¹₃-degrees

1996/08/06 by Philip Welch, Welch, Philip
Computer Science · Decision Sciences · Economics, Econometrics and Finance · #Computability, Logic, AI Algorithms #Economic theories and models #FOS: Mathematics #Game Theory and Applications #Logic (math.LO)

paper · pdf · doi:10.48550/arxiv.math/9608203

openalex publication_date 1996/08/06 · openalex created_date 2022/09/30 · openalex updated_date 2026/07/28

Abstract

Let D = d_n be a countable collection of Delta¹₃ degrees. Assuming that all co-analytic games on integers are determined (or equivalently that all reals have ``sharps''), we prove that either D has a Delta¹₃-minimal upper bound, or that for any n, and for every real r recursive in d_n, games in the pointclasses Delta¹₂(r) are determined. This is proven using Core Model theory.

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