Some Applications of Coarse Inner Model Theory
Hjorth, Greg
J. Symbolic Logic, Tome 62 (1997) no. 1, p. 337-365 / Harvested from Project Euclid
The Martin-Steel coarse inner model theory is employed in obtaining new results in descriptive set theory. $\underset{\sim}{\Pi}$ determinacy implies that for every thin $\Sigma^1_2$ equivalence relation there is a $\Delta^1_3$ real, $N$, over which every equivalence class is generic--and hence there is a good $\Delta^1_2(N^\sharp)$ wellordering of the equivalence classes. Analogous results are obtained for $\Pi^1_2$ and $\Delta^1_2$ quasilinear orderings and $\underset{\sim}{\Pi}^1_2$ determinacy is shown to imply that every $\Pi^1_2$ prewellorder has rank less than $\underset{\sim}{\delta}^1_2$.
Publié le : 1997-06-14
Classification:  Inner model theory,  large cardinals,  equivalent relations
@article{1183745232,
     author = {Hjorth, Greg},
     title = {Some Applications of Coarse Inner Model Theory},
     journal = {J. Symbolic Logic},
     volume = {62},
     number = {1},
     year = {1997},
     pages = { 337-365},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1183745232}
}
Hjorth, Greg. Some Applications of Coarse Inner Model Theory. J. Symbolic Logic, Tome 62 (1997) no. 1, pp.  337-365. http://gdmltest.u-ga.fr/item/1183745232/