%0 Journal Article %T On club-like principles on regular cardinals above $\beth_¦Ø$ %A Mirna D£¿amonja %J Mathematics %D 2006 %I arXiv %X We prove that for regular $\lambda$ above a strong limit singular $\mu$ certain guessing principles follow just from cardinal arithmetic assumptions. The main result is that for such $\lambda$ and $\mu$ there are coboundedly many regular $\kappa<\mu$ such that $\clubsuit^-(S^\lambda_\kappa)$ holds whenever $\lambda=\lambda^{<\kappa}$. %U http://arxiv.org/abs/math/0608638v1