Kunen and set theory
نویسنده
چکیده
Kenneth Kunen (1943–) figured principally in the development of set theory in all the major directions, this during a formative period for the subject when it was transmuting to a sophisticated field of mathematics. In fact, several of Kunen’s results and proofs still frame modern set theory or serve as standards to be reckoned with in its further progress. This is all the more notable as much of the work was done in a short run of about four years from his 1968 thesis. The work has an incisiveness and technical virtuosity remarkable for the time as well as a sense of maturity and definiteness. Typically, others may have started a train of conceptual constructions, but Kunen made great leaps forward advancing the subjects, almost heroically, to what would seem to be the limits achievable at the time. There is a sense of movement from topic to topic and then beyond to applications of set theory, with heights scaled and more heights beckoning. In what follows, we chronicle Kunen’s singular progress over the broad swath of set theory. The work of the years 1968–1972, especially, deserve full airing, and we recall the initiatives of the time as well as describe the ramifications of the advances made. As almost all of this work is in the mainstream of modern set theory, we only set the stage in a cursory way and recall the most immediately relevant concepts, relying in part on the readers’ familiarity,2 but then dwell on the particulars of how ideas and proofs became method. In this way we reaffirm Kunen’s work in set theory as central to the subject and of lasting significance for its development.
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A Model in Which There Are Jech–kunen Trees but There Are No Kurepa Trees
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