length $\theta$ are in ${{{\mathbb P}^\theta_\lambda}}$, we will be bound to declare that the amalgamation is in our forcing notion. The amalgamation (and natural limits) will be the only way to build new conditions from the old ones, but the description above still misses an important factor. So far, a condition does not have to know what are the reasons for it to be called to ${{{\mathbb P}^\theta_\lambda}}$. This information is [*the history of the condition*]{} and it will be encoded by two functions $h^p,g^p$. (Actually, these functions will give histories of all elements of $u^p$ describing why and how those points were incorporated to $u^p$. Thus both functions will be defined on $u^p\times{{\rm ht}}(p)$, were ${{\rm ht}}(p)$ is the height of the condition $p$, that is the step in our construction at which the condition $p$ is created.) We will also want that our forcing is suitably closed, and getting “$({<}\lambda)$–strategically closed” would be fine. To make that happen we will have to deal with two relations on on ${{{\mathbb P}^\theta_\lambda}}$: $\leq_{\rm pr}$ and $\leq$. The first (“pure”) is $({<}\lambda)$–closed and it will help in getting the strategic closure of the second (main) one. In some sense, the relation 