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Forcing a set model of + Harrington's Principle

Forcing a set model of + Harrington's Principle

Let denote third order arithmetic. Let Harrington's Principle, , denote the statement that there is a real x such that every x ā€admissible ordinal is a cardinal in . In this paper, assuming there exists a remarkable cardinal with a weakly inaccessible cardinal above it, we force a set model ā€¦