Many forcing notions obtained using the creature technology are naturally connected with certain integer games.

The paper contains a self-contained alternative proof of my Theorem in Characterization of generic extensions of models of set theory, Fund. Math. 83 (1973), 35–46, saying that for models $M\subseteq N$ of ZFC with same ordinals, the condition $Ap{r}_{M,N}\left(\kappa \right)$ implies that $N$ is a $\kappa$-C.C. generic extension of $M$.

[1] T. Bartoszyński, Additivity of measure implies additivity of category, Trans. Amer. Math. Soc. 281 (1984), 209-213. [2] T. Bartoszyński and H. Judah, Measure and Category, in preparation. [3] D. H. Fremlin, Cichoń’s diagram, Publ. Math. Univ. Pierre Marie Curie 66, Sém. Initiation Anal., 1983/84, Exp. 5, 13 pp. [4] M. Goldstern, Tools for your forcing construction, in: Set Theory of the Reals, Conference of Bar-Ilan University, H. Judah (ed.), Israel Math. Conf. Proc. 6, 1992, 307-362. [5] H....

We present principles for guessing clubs in the generalized club filter on ${}_{\kappa }\lambda$. These principles are shown to be weaker than classical diamond principles but often serve as sufficient substitutes. One application is a new construction of a λ⁺-Suslin-tree using assumptions different from previous constructions. The other application partly solves open problems regarding the cofinality of reflection points for stationary subsets of ${\left[\lambda \right]}^{\aleph ₀}$.