Two Results on Borel Orders
Louveau, Alain
J. Symbolic Logic, Tome 54 (1989) no. 1, p. 865-874 / Harvested from Project Euclid
We prove two results about the embeddability relation between Borel linear orders: For $\eta$ a countable ordinal, let $2^\eta$ (resp. $2^{<\eta}$) be the set of sequences of zeros and ones of length $\eta$ (resp. $<\eta$), equipped with the lexicographic ordering. Given a Borel linear order $X$ and a countable ordinal $\xi$, we prove the following two facts. (a) Either $X$ can be embedded (in a $\triangle^1_1(X,\xi)$ way) in $2^{\omega\xi}$, or $2^{\omega\xi + 1}$ continuously embeds in $X$. (b) Either $X$ can embedded (in a $\triangle^1_1(X,\xi)$ way) in $2^{\omega\xi}$, or $2^{\omega\xi}$ continuously embeds in $X$. These results extend previous work of Harrington, Shelah and Marker.
Publié le : 1989-09-14
Classification: 
@article{1183743023,
     author = {Louveau, Alain},
     title = {Two Results on Borel Orders},
     journal = {J. Symbolic Logic},
     volume = {54},
     number = {1},
     year = {1989},
     pages = { 865-874},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1183743023}
}
Louveau, Alain. Two Results on Borel Orders. J. Symbolic Logic, Tome 54 (1989) no. 1, pp.  865-874. http://gdmltest.u-ga.fr/item/1183743023/