Is there a nice and simple paper which summarizes the definitions and properties of strong logics? When I say strong logics I mean something like stationary logic, or Magidor-Malitz quantifier, $\cal L_{\kappa,\lambda}$, etc.
What I am looking for is a paper without many proofs (although preferably with some proofs, just to get the idea) which gives out the definitions of the various extensions of first-order logic, and outlines their properties (compactness, completeness) and differences.
Of course a combination of several short papers is also welcomed, but I really wish to avoid (for now) the long and technical expositions on each logic.
I want to say out that at this moment I am particularly interested in the three logics mentioned above, the stationary logic, MM-quantifier, and $\cal L_{\kappa,\lambda}$ logics. Other types of strong logics are very welcomed, but those three are currently the main points of interest.