, Volume 131, Issue 1, pp 61-99

Indexed squares

Rent the article at a discount

Rent now

* Final gross prices may vary according to local VAT.

Get Access


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.

First author partially supported by NSF grants DMS-9703945 and DMS-0070549.
Second author partially supported by NSF Grants DMS-9305990, DMS-9712580, DMS-9996280 and DMS-0088948.