Algebraic Methods and Bounded Formulas Domenico Zambella Abstract: We present some algebraic tools and apply them to the study of the expressive power of bounded formulas in secondÂorder arithmetic. The accent is on negative results. The techniques studied here come from Boolean circuit complexity and are adapted to the context of arithmetic. One of the purposes of these article is to expose them to a public with interests ranging from arithmetic to finite model theory. Our exposition is selfÂcontained.