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The Σ21 theory of axioms of symmetry

Published online by Cambridge University Press:  12 March 2014

Galen Weitkamp
Galen Weitkamp*
Affiliation:
Department of Mathematics, Western Illinois University, Macomb, Illinois 61455
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Abstract

The axiom of symmetry (Aℵ0) asserts that for every function F: ω2 → ω2 there is a pair of reals x and y in ω2 so that y is not in the countable set {(F(x))n: n< ω} coded by F(x) and x is not in the set coded by F(y). A(Γ) denotes axiom Aℵ0 with the restriction that graph(F) belongs to the pointclass Γ. In §2 we prove A(). In §3 we show A(), A() and ω2 ⊈ L are equivalent. In §4 several effective versions of A(REC) are examined.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 54 , Issue 3 , September 1989 , pp. 727 - 734
Copyright
Copyright © Association for Symbolic Logic 1989

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