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A univalent formalization of the p-adic numbers

Published online by Cambridge University Press:  13 February 2015

ÁLVARO PELAYO ,
VLADIMIR VOEVODSKY  and
MICHAEL A. WARREN
ÁLVARO PELAYO
Affiliation:
Department of Mathematics, University of California, San Diego, 9500 Gilman Dr #0112, La Jolla, California 92093-0112, U.S.A. Email: alpelayo@math.ucsd.edu School of Mathematics, Institute for Advanced Study, Einstein Drive, Princeton, New Jersey 08540, U.S.A. Email: vladimir@ias.edu
VLADIMIR VOEVODSKY
Affiliation:
School of Mathematics, Institute for Advanced Study, Einstein Drive, Princeton, New Jersey 08540, U.S.A. Email: vladimir@ias.edu
MICHAEL A. WARREN
Affiliation:
Los Angeles, California, U.S.A. Email: maw@mawarren.net
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Abstract

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The goal of this paper is to report on a formalization of the p-adic numbers in the setting of the second author's univalent foundations program. This formalization, which has been verified in the Coq proof assistant, provides an approach to the p-adic numbers in constructive algebra and analysis.

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