Abstract
AbstractThis paper concerns the theory of morasses. In the early 1970s Jensen defined (k, α)-morasses for uncountable regular cardinals k and ordinals α < k. In the early 1980s Velleman defined (k, 1)-simplified morasses for all regular cardinals k. He showed that there is a (k, 1)-simplified morass if and only if there is (k, 1)-morass. More recently he defined (k, 2)-simplified morasses and Jensen was able to show that if there is a (k, 2)-morass then there is a (k, 2)-simplified morass.In this paper we prove the converse of Jensen's result, i.e., that if there is a (k, 2)-simplified morass then there is a (k, 2)-morass.
Publisher
Cambridge University Press (CUP)
Reference10 articles.
1. Stanley L. , A short course on gap-one morasses and a review of the fine structure of L in “Surveys in set theory”, (A. R. D. Mathias, editor), London Mathematical Society Lecture Notes Series, vol. 87, 1982, pp. 197–243.
2. Simplified Gap-2 morasses
3. Dodd A. , Constructibility, two cardinals problems and the gap-n theorems, M. sc. dissertation , Oxford, 1974.
4. Devlin K. , Higher gap morasses, Ib: Finite gap morasses—the general case, in preparation, 1993.
Cited by
5 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献
1. On constructions with 2-cardinals;Archive for Mathematical Logic;2017-05-15
2. Forcings constructed along morasses;The Journal of Symbolic Logic;2011-12
3. Large semilattices of breadth three;Fundamenta Mathematicae;2010
4. Σ* Fine Structure;Handbook of Set Theory;2009-12-10
5. A topological application of flat morasses;Fundamenta Mathematicae;2007