Games and Trees in Infinitary Logic: A Survey
نویسنده
چکیده
We describe the work and underlying ideas of the Helsinki Logic Group in infinitary logic. The central idea is to use trees and Ehrenfeucht-Fräıssé games to measure differences between uncountable models. These differences can be expressed by sentences of so-called infinitely deep languages. This study has ramified to purely set-theoretical problems related to properties of trees, descriptive set theory in 1ω1, detailed study of transfinite Ehrenfeucht-Fräıssé games, new constructions of uncountable models, non-well-founded induction, infinitely deep languages, non-structure theorems, and stability theory. The aim of this paper is to give an overview of the underlying ideas of this reasearch together with a survey of the main results.
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