From algebra to analysis: New proofs of theorems by Ritt and Seidenberg

Ritt’s theorem of zeroes and Siedenberg’s embedding are classical results in differential algebra allowing to connect algebraic model-theoretic on nonlinear PDEs the realm analysis. However, existing proofs these use sophisticated tools from constructive (characteristic set theory) analysis (Riquier’s existence theorem). In this paper, we give new short for both theorems relying only basic facts Cauchy-Kovalevskaya PDEs.