Square and club-guessing orientation

For a set $S$ of nonzero limit ordinals below a regular uncountable $\kappa$, a $C$-sequence on $S$ assigns a club $C_{\delta }\subseteq \delta$ to each $\delta \in S$. One possible club-guessing requirement is that for every club $D\subseteq \kappa$, the set $\{\delta \in S:C_{\delta }\subseteq D\}$ is stationary. This describes a requirement, not an existence assertion.

A typical coherence requirement is $C_{\beta }=C_{\delta }\cap \beta$ whenever $\beta$ is a nonzero limit point of $C_{\delta }$ (and the indices in question are in the domain). Square principles combine coherence with precisely specified domain, order-type, width, or no-thread conditions. A thread means a club $D$ whose initial segments agree with the prescribed clubs at its limit points. These qualifications are part of the principle; coherence alone is not a square principle. The later trees, delta-systems, and diamond track supplies the formal versions. No square or club-guessing existence theorem is used here.