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Generic compactness reformulated

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We point out a connection between reflection principles and generic large cardinals. One principle of pure reflection is introduced that is as strong as generic supercompactness of ω2 by Σ-closed forcing. This new concept implies CH and extends the reflection principles for stationary sets in a canonical way.

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Correspondence to Bernhard König.

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Mathematics Subject Classification (2000): 03E50, 03E55

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König, B. Generic compactness reformulated. Arch. Math. Logic 43, 311–326 (2004). https://doi.org/10.1007/s00153-003-0211-1

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