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Indexed squares. (English) Zbl 1025.03040

Summary: We study some combinatorial principles intermediate between square and weak square. We construct models which distinguish various square principles, and show that a strengthened form of weak square holds in the Prikry model. Jensen proved that a large cardinal property slightly stronger than 1-extendibility is incompatible with square; we prove this is close to optimal by showing that 1-extendibility is compatible with square.

MSC:

03E05 Other combinatorial set theory
03E55 Large cardinals
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