The $\sum^1_2$ Theory of Axioms of Symmetry
Weitkamp, Galen
J. Symbolic Logic, Tome 54 (1989) no. 1, p. 727-734 / Harvested from Project Euclid
The axiom of symmetry $(A_{\aleph_0})$ asserts that for every function $F: ^\omega 2 \rightarrow ^\omega 2$ there is a pair of reals $x$ and $y$ in $^\omega 2$ so that $y$ is not in the countable set $\{(F(x))_n:n < \omega\}$ coded by $F(x)$ and $x$ is not in the set coded by $F(y). A(\Gamma)$ denotes axiom $A_{\aleph_0}$ with the restriction that $\text{graph}(F)$ belongs to the pointclass $\Gamma$. In $\S 2$ we prove $A(\Sigma^1_1)$. In $\S 3$ we show $A(\Pi^1_1), A(\Sigma^1_2)$ and $^\omega 2 \nsubseteq L$ are equivalent. In $\S 4$ several effective versions of $A(\mathrm{REC})$ are examined.
Publié le : 1989-09-14
Classification: 
@article{1183743012,
     author = {Weitkamp, Galen},
     title = {The $\sum^1\_2$ Theory of Axioms of Symmetry},
     journal = {J. Symbolic Logic},
     volume = {54},
     number = {1},
     year = {1989},
     pages = { 727-734},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1183743012}
}
Weitkamp, Galen. The $\sum^1_2$ Theory of Axioms of Symmetry. J. Symbolic Logic, Tome 54 (1989) no. 1, pp.  727-734. http://gdmltest.u-ga.fr/item/1183743012/