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A GENERALIZED CANTOR THEOREM IN $\mathsf {ZF}$

Part of: Set theory

Published online by Cambridge University Press:  14 March 2022

YINHE PENG  and
GUOZHEN SHEN Open the ORCID record for GUOZHEN SHEN [Opens in a new window]
YINHE PENG
Affiliation:
ACADEMY OF MATHEMATICS AND SYSTEMS SCIENCE CHINESE ACADEMY OF SCIENCES EAST ZHONG GUAN CUN ROAD NO. 55 BEIJING 100190, CHINA E-mail: pengyinhe@amss.ac.cn
GUOZHEN SHEN*
Affiliation:
SCHOOL OF PHILOSOPHY WUHAN UNIVERSITY NO. 299, BAYI ROAD WUHAN 430072, HUBEI PROVINCE, CHINA
*
E-mail: shen_guozhen@outlook.com
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Abstract

It is proved in $\mathsf {ZF}$ (without the axiom of choice) that, for all infinite sets M, there are no surjections from $\omega \times M$ onto $\operatorname {\mathrm {\mathscr {P}}}(M)$.

Keywords

ZFCantor’s theoremsurjectionaxiom of choice

MSC classification

Primary: 03E10: Ordinal and cardinal numbers
Secondary: 03E25: Axiom of choice and related propositions
Type
Article
Information
The Journal of Symbolic Logic , Volume 89 , Issue 1 , March 2024 , pp. 204 - 210
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Copyright
© The Author(s), 2022. Published by Cambridge University Press on behalf of The Association for Symbolic Logic

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