I dont know specifically about iwasawa theory but new applications of model theory to algebra and algebraic geometry were recently developed in a series of papers by kazhdan and hrushovki for example their paper integration in valued fields is a top of an iceberg van den dries has excellent notes on this paper on his website. The similarity between model theory and algebraic geometry is sup ported by how a great deal of the applications of model theory have been in algebra in this paper we prove several theorems of algebraic geometry using model theoretic approaches and exhibit the approach of proving theorems about mathematical objects by analysis of lan. Buy model theory and algebraic geometry an introduction to e hrushovskis proof of the geometric mordell lang conjecture lecture notes in mathematics on amazoncom free shipping on qualified orders. On the wikipedia article for model theory it says that a modern definition of model theory is model theory algebraic geometry fields and cites hodges wilfrid 1997 a shorter model theory
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