Marcia Groszek
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Marcia Jean Groszek is an American mathematician whose research concerns mathematical logic, set theory, forcing, and recursion theory. She is a professor of mathematics at Dartmouth College.[1]
As a high school student, Groszek felt isolated for her interest in mathematics, but she found a sense of community through her participation in the Hampshire College Summer Mathematics Program,[2] and she went on to earn her bachelor's degree at Hampshire College.[1] She completed her Ph.D. in 1981 at Harvard University. Her dissertation, Iterated Perfect Set Forcing and Degrees of Constructibility, was supervised by Akihiro Kanamori.[3]
Research
With Theodore Slaman, Groszek showed that (if they exist at all) non-constructible real numbers must be widespread, in the sense that every perfect set contains one of them, and they asked analogous questions of the non-computable real numbers.[4][C] With Slaman, she has also shown that the existence of a maximally independent set of Turing degrees, of cardinality less than the cardinality of the continuum, is independent of ZFC.[A]
In the theory of ordinal definable sets, an unordered pair of sets is said to be a Groszek–Laver pair if the pair is ordinal definable but neither of its two elements is; this concept is named for Groszek and Richard Laver, who observed the existence of such pairs in certain models of set theory.[5][B]
