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Durham University

Computer Science


Publication details for Professor Iain Stewart

Stewart, I.A. (1999). A perspective on Lindström quantifiers and oracles. In Generalized Quantifiers and Computation: 9th European Summer School in Logic, Language, and Information ESSLLI’97Workshop Aix-en-Provence, France, August 11–22, 1997 Revised Lectures. Väänänen, J. Berlin: Springer. Lecture Notes in Computer Science Vol. 1754: 51-71.

Author(s) from Durham


This paper presents a perspective on the relationship between Lindström quantifiers in model theory and oracle computations in complexity theory. We do not study this relationship here in full generality (indeed, there is much more work to do in order to obtain a full appreciation), but instead we examine what amounts to a thread of research in this topic running from the motivating results, concerning logical characterizations of nondeterministic polynomial-time, to the consideration of Lindström quantifiers as oracles, and through to the study of some naturally arising questions (and subsequent answers). Our presentation follows the chronological progress of the thread and highlights some important techniques and results at the interface between finite model theory and computational complexity theory.