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Keywords Analytic sets Automatic continuity Computable presentations Continuous logic Effective completeness Lusin's Theorem Metric structures Polish group, Non-singular transformation approximation algorithms, polynomial-time approximation scheme, traveling salesperson problem, analyst traveling salesman problem co-analytic sets collapsing hierarchy computability computable analysis infinite measure-preserving transformation intuitionistic separation theorems model theory, von Neumann algebra, free entropy, random matrix, strongly 1-bounded, ultraproduct nonstandard analysis o-minimal structures, log-analytic functions, exponential number, preparation theorems proof mining pseudo-arc solenoid