Indexed squares

James Cummings, Ernest Schimmerling
2002 Israel Journal of Mathematics  
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 1extendibility is incompatible with square; we prove this is close to optimal by showing that 1-extendibility is compatible with square.
doi:10.1007/bf02785851 fatcat:zxwn7e7x45hgxd6hyt77m72qxq