A COMPARISON OF VARIOUS ANALYTIC CHOICE PRINCIPLES
Copyright policy )A COMPARISON OF VARIOUS ANALYTIC CHOICE PRINCIPLES
AbstractWe investigate computability theoretic and descriptive set theoretic contents of various kinds of analytic choice principles by performing a detailed analysis of the Medvedev lattice of $\Sigma ^1_1$ -closed sets. Among others, we solve an open problem on the Weihrauch degree of the parallelization of the $\Sigma ^1_1$ -choice principle on the integers. Harrington’s unpublished result on a jump hierarchy along a pseudo-well-ordering plays a key role in solving this problem.
FOS: Computer and information sciences, Computer Science - Logic in Computer Science, Mathematics - Logic, arithmetical transfinite recusion, Foundations of classical theories (including reverse mathematics), Hierarchies of computability and definability, Weihrauch reducibility, \( \Sigma^1_1\)-choice, Logic in Computer Science (cs.LO), FOS: Mathematics, Other degrees and reducibilities in computability and recursion theory, Logic (math.LO), Descriptive set theory
FOS: Computer and information sciences, Computer Science - Logic in Computer Science, Mathematics - Logic, arithmetical transfinite recusion, Foundations of classical theories (including reverse mathematics), Hierarchies of computability and definability, Weihrauch reducibility, \( \Sigma^1_1\)-choice, Logic in Computer Science (cs.LO), FOS: Mathematics, Other degrees and reducibilities in computability and recursion theory, Logic (math.LO), Descriptive set theory
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