Vol. 28, No. 1, 1969

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A unifying condition for implications among the axioms of choice for finite sets

Martin Michael Zuckerman

Vol. 28 (1969), No. 1, 233–242
Abstract

For n 1, let C(n) be the axiom of choice restricted to sets of n-element sets. We define a condition, (Z), which is sufficient to assure the provability of an implication

(C (m1 )&C (m2 )&⋅⋅⋅&C (ms)) → C(n)

in set theory. We compare condition (Z) with various other conditions related to the above implication.

Mathematical Subject Classification
Primary: 02.60
Secondary: 05.00
Milestones
Received: 8 September 1967
Published: 1 January 1969
Authors
Martin Michael Zuckerman