Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



The law of infinite cardinal addition is weaker than the axiom of choice

Authors: J. D. Halpern and Paul E. Howard
Journal: Trans. Amer. Math. Soc. 220 (1976), 195-204
MSC: Primary 02K20; Secondary 02K05
MathSciNet review: 0409183
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We construct a permutation model of set theory with urelements in which $ {C_2}$ (the choice principle restricted to families whose elements are unordered pairs) is false but the principle, ``For every infinite cardinal m, $ 2m = m$'' is true. This answers in the negative a question of Tarski posed in 1924. We note in passing that the choice principle restricted to well-ordered families of finite sets is also true in the model.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 02K20, 02K05

Retrieve articles in all journals with MSC: 02K20, 02K05

Additional Information

Article copyright: © Copyright 1976 American Mathematical Society

American Mathematical Society