SQUARE WITH BUILT-IN DIAMOND-PLUS.

We formulate combinatorial principles that combine the square principle with various strong forms of the diamond principle, and prove that the strongest amongst them holds in L for every infinite cardinal.As an application, we prove that the following two hold in L:1.For every infinite regular cardinal λ, there exists a special λ+-Aronszajn tree whose projection is almost Souslin;2.For every infinite cardinal λ, there exists a respecting λ+-Kurepa tree; Roughly speaking, this means that this λ+-Kurepa tree looks very much like the λ+-Souslin trees that Jensen constructed in L. [ABSTRACT FROM PUBLISHER]