Composition Methods and its applications
Here are some articles which we might study
Shelah
The Monadic Theory of Order.
Makowsky
Algorithmic Uses of The Feferman-Vaught Theorem.
Feferman Vaught.
The first-order properties of products of algebraic systems.
Sees.
The structure of the models of decidable monadic theories of graphs.
Lifsches and Shelah.
Uniformization and Skolem Functions in the Class of Trees.
Lifsches+Shelah,
Random Graphs in the monadic theory of order
-- Archive for Math Logic 38 (1999) 273-312
+Shelah,
On the very weak $0-1$ law for random graphs with orders -- J
Logic and Computation 6 (1996) 137-159
Fisher and Makowsky.
On Spectra of Sentences of Monadic second order logic with counting.
Walukiewicz.
Monadic Second-orde Logic on tree like structures .
A. Rabinovich and S. Maoz
An Infinite Hierarchy of Temporal Logics over Branching Time.
Information and Computation, 171:306-332, 2001.
F. Moller and A. Rabinovich
Counting on CTL*: on the expressive power of monadic path logic.
Information and Computation 184(2003)147-159.
A. Rabinovich
Selection and Uniformization in Generalized Product
Logic J. of IGPL, 12:125-134,2004.
A. Rabinovich
Composition Theorem for Generalized Sum
Amit
Tal .