TY - JOUR
T1 - Measurable Selections
T2 - A Bridge between Large Cardinals and Scientific Applications?
AU - Burgess, John P.
N1 - Publisher Copyright:
© 2021 The Author. Published by Oxford University Press. All rights reserved.
PY - 2021/10/1
Y1 - 2021/10/1
N2 - There is no prospect of discovering measurable cardinals by radio astronomy, but this does not mean that higher set theory is entirely irrelevant to applied mathematics broadly construed. By way of example, the bearing of some celebrated descriptive-set-theoretic consequences of large cardinals on measurable-selection theory, a body of results originating with a key lemma in von Neumann's work on the mathematical foundations of quantum theory, and further developed in connection with problems of mathematical economics, will be considered from a philosophical point of view.
AB - There is no prospect of discovering measurable cardinals by radio astronomy, but this does not mean that higher set theory is entirely irrelevant to applied mathematics broadly construed. By way of example, the bearing of some celebrated descriptive-set-theoretic consequences of large cardinals on measurable-selection theory, a body of results originating with a key lemma in von Neumann's work on the mathematical foundations of quantum theory, and further developed in connection with problems of mathematical economics, will be considered from a philosophical point of view.
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U2 - 10.1093/philmat/nkab016
DO - 10.1093/philmat/nkab016
M3 - Article
AN - SCOPUS:85117420434
SN - 0031-8019
VL - 29
SP - 353
EP - 365
JO - Philosophia Mathematica
JF - Philosophia Mathematica
IS - 3
ER -