On the Quasi-Ordering of Borel Linear Orders Under Embeddability

Louveau, Alain; Saint-Raymond, Jean

J. Symbolic Logic, Tome 55 (1990) no. 1, p. 537-560 / Harvested from Project Euclid

Résumé

We provide partial answers to the following problem: Is the class of Borel linear orders well-quasi-ordered under embeddability? We show that it is indeed the case for those Borel orders which are embeddable in $\mathbf{R}^\omega$, with the lexicographic ordering. For Borel orders embeddable in $\mathbf{R}^2$, our proof works in ZFC, but it uses projective determinacy for Borel orders embeddable in some $\mathbf{R}^n, n < \omega$, and hyperprojective determinacy for the general case.

Publié le : 1990-06-14
Classification:

@article{1183743312,
     author = {Louveau, Alain and Saint-Raymond, Jean},
     title = {On the Quasi-Ordering of Borel Linear Orders Under Embeddability},
     journal = {J. Symbolic Logic},
     volume = {55},
     number = {1},
     year = {1990},
     pages = { 537-560},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1183743312}
}

Louveau, Alain; Saint-Raymond, Jean. On the Quasi-Ordering of Borel Linear Orders Under Embeddability. J. Symbolic Logic, Tome 55 (1990) no. 1, pp.  537-560. http://gdmltest.u-ga.fr/item/1183743312/