Adrian Mathias: Difference between revisions
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* [https://www.dpmms.cam.ac.uk/~ardm/ Home page] |
* [https://www.dpmms.cam.ac.uk/~ardm/ Home page] |
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* [https://genealogy.math.ndsu.nodak.edu/id.php?id=24586 Adrian Richard David Mathias] at the [[Mathematics Genealogy Project]] |
* [https://genealogy.math.ndsu.nodak.edu/id.php?id=24586 Adrian Richard David Mathias] at the [[Mathematics Genealogy Project]] |
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[[Category:20th-century mathematicians]] |
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[[Category:21st-century mathematicians]] |
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[[Category:1944 births]] |
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[[Category:Living people]] |
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[[Category:Set theorists]] |
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Revision as of 20:06, 9 February 2020
Adrian R. D. Mathias | |
|---|---|
| Born | February 12, 1944 |
| Nationality | Welsh |
| Alma mater | University of Cambridge |
| Scientific career | |
| Fields | Mathematics |
| Institutions | University of Cambridge Université de la Réunion |
| Doctoral advisor | Ronald Jensen John Horton Conway |
| Doctoral students | James Cummings Thomas Forster Akihiro Kanamori |
Adrian Richard David Mathias (born 12 February 1944) is a Welsh mathematician working in set theory. The forcing notion Mathias forcing is named for him.
Work
Mathias became mathematically active soon after the introduction of forcing by Paul Cohen, and Kanamori[1] credits his survey of forcing that was eventually published as Surrealist landscape with figures[2] as being a "vital source" on forcing in its early days. His paper Happy families[3], extending his 1968 Cambridge thesis, proves important properties of the forcing now known as Mathias forcing. In the same paper he shows that no (infinite) maximal almost disjoint family can be analytic. Mathias also used forcing to separate two weak forms of the Axiom of choice, showing that the ordering principle, which states that any set can be linearly ordered, does not imply the Boolean Prime Ideal Theorem[4]. His more recent work on forcing includes the study of the theory PROVI of provident sets, a minimalist axiom system that still allows the forcing construction to proceed[5].
Mathias is also known for his writings around sociological aspects of logic. These include The ignorance of Bourbaki and Hilbert, Bourbaki and the scorning of logic, in which Mathias criticises Bourbaki's approach to logic; in A Term of Length 4,523,659,424,929 he shows that the number in the title is the number of symbols required for Bourbaki's definition of the number 1. Mathias has also considered claims that standard ZFC is stronger than necessary for "mainstream" mathematics; his paper What is Mac Lane missing? on this topic appeared alongside Saunders Mac Lane's response Is Mathias an ontologist?. Mathias also conducted a detailed study of the strength of a weakened system suggested by Mac Lane[6].
References
- ^ Kanamori, Akihiro (2003). The Higher Infinite. Berlin: Springer. p. 117. ISBN 3-540-00384-3.
- ^ Mathias, Adrian. "Surrealist landscape with figures". Periodica Hungarica. 10: 109--175.
- ^ Mathias, Adrian (1977). "Happy Families". Annals of Mathematical Logic. 12: 59--111.
- ^ Jech, Thomas (2008). The Axiom of Choice. Mineola, New York: Dover. p. 117. ISBN 978-0-486-46624-8.
- ^ Mathias, Adrian (2015). "Provident sets and rudimentary set forcing". Fundamenta Mathematicæ. 230: 99--148.
- ^ Mathias, Adrian (2001). "The Strength of Mac Lane Set Theory". Annals of Pure and Applied Logic. 110: 107--234.