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In September of 1959, at the conference on Infinitistic Methods in Warsaw,Ernst Specker presented a joint paper with Robert MacDowell in which theauthors proved that every model of Peano Arithmetic has an elementary extensionsuch that all new elements are larger than all elements of the model. Untilnow, the theorem has been a constant source of new results and generalizations,and there are still open problems related to it. This paper is a survey of allthose developments.

63 Years of the MacDowell-Specker Theorem