The Fine Structure of Real Mice
Cunningham, Daniel W.
J. Symbolic Logic, Tome 63 (1998) no. 1, p. 937-994 / Harvested from Project Euclid
Before one can construct scales of minimal complexity in the Real Core Model, K($\mathbb{R}$), one needs to develop the fine-structure theory of K($\mathbb{R}$). In this paper, the fine structure theory of mice, first introduced by Dodd and Jensen, is generalized to that of real mice. A relative criterion for mouse iterability is presented together with two theorems concerning the definability of this criterion. The proof of the first theorem requires only fine structure; whereas, the second theorem applies to real mice satisfying AD and follows from a general definability result obtained by abstracting work of John Steel on L($\mathbb{R}$). In conclusion, we discuss several consequences of the work presented in this paper relevant to two issues: the complexity of scales in K(R) and the strength of the theory ZF + AD + $\neg DC_\mathbb{R}$.
Publié le : 1998-09-14
Classification: 
@article{1183745575,
     author = {Cunningham, Daniel W.},
     title = {The Fine Structure of Real Mice},
     journal = {J. Symbolic Logic},
     volume = {63},
     number = {1},
     year = {1998},
     pages = { 937-994},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1183745575}
}
Cunningham, Daniel W. The Fine Structure of Real Mice. J. Symbolic Logic, Tome 63 (1998) no. 1, pp.  937-994. http://gdmltest.u-ga.fr/item/1183745575/