Square principles with tail-end agreement

This paper investigates the principles ta λ,δ, weakenings of λ which allow δ many clubs at each level but require them to agree on a tail-end. First, we prove that ta λ,<ω implies λ. Then, by forcing from a model with a measurable cardinal, we show that λ,2 does not imply ta λ,δ for regular λ, and ta δ+,δ does not imply δ+,<δ. With a supercompact cardinal the former result can be extended to singular λ, and the latter can be improved to show that ta λ,δ does not imply λ,<δ for δ < λ.