Higher gap morasses [Elektronische Ressource] / von Franqui Cárdenas

Higher gap morassesDISSERTATIONzur Erlangung des akademischen Gradesdoctor rerum naturalium(Dr. rer. nat.)im Fach Mathematikeingereicht an derMathematisch-Naturwissenschaftlichen Fakulta¨t IHumboldt-Universita¨t zu BerlinvonMaster.-Math. Franqui C´ardenasgeboren am 26.12.1974 in Villavicencio, KolumbienPra¨sident der Humboldt-Universita¨t zu Berlin:Prof. Dr. J. MlynekDekan der Mathematisch-Naturwissenschaftlichen Fakultat I:¨Prof. Dr. U. Kuchler¨Gutachter:1) Prof. Dr. Ronald Jensen2) Prof. Dr. Kai Hauser3) Dr. Sc. E. Herrmanneingereicht am: 31. August 2004Tag der mundlichen Prufung: 6. Juni 2005¨ ¨AbstractVelleman in [Velleman(1987)] proved the consistency of the existence of sim-pli fied gap 2 morasses (equivalent to the concrete morasses defined byJensen) using a two stage forcing. We gave an essentially different proofof the same result and fill up some details from the Velleman’s paper whichwere not clear. In fact the proof uses a slightly simpler and different defin-ition of gap two simplified morasses and of the forcing conditions. We haveeliminated the use of square-like sequences in the second stage, employinginstead a“guessing”procedure for requirement. With these steps we hope tohave laid the foundation for a future proof of gap n morasses in ZFC.