The work of Andrzej Mostowski in model theory

Publisher Summary This chapter focuses on the work of Andrzej Mostowski in model theory. Mostowski regarded model theory basically as a tool for other investigations in the foundations of mathematics. The chapter describes the theory of indiscernible elements, created jointly with Andrzej Ehrenfeucht, the theory of products, and generalized quantifiers. It discusses seven papers in which Mostowski published the results of his investigations in model theory. The paper “On direct products of theories”, published in 1952, begins with the statement that it concerns decidability questions. Mostowski's method of reducing the question about the truth of a sentence in a product to a similar question for factors was extended in a paper by R. L. Vaught and then in one by S. Feferman and R. L. Vaught. Ehrenfeucht's and Mostowski's paper on automorphisms investigations in model theory were concentrated on the characterization of sentences invariant with respect to various operations. The main problem investigated by Ehrenfeucht and Mostowski was that of the existence of models with a large group of automorphisms.