Abstract
In the present paper we explore partition properties of admissible ordinals. In §2 the connection between partition properties, collection, separation and reflection principles is studied. In §3 we give characterizations of partition properties which are satisfied by certain definable subsets of κ. Covering properties, which are studied in §4, are a convenient generalization of partition properties and are used to investigate the strength of certain partition properties of κ. Finally in §5 we study the definability of the homogeneous set in partitions of exponent greater than one.
The author is grateful to the Minna-James-Heineman Stiftung, Hannover, for its financial support during the preparation of the present paper at the Universität Heidelberg.
Some of the results of the present paper have also appeared in the author's 1983 Oxford doctoral thesis. He was assisted by an award from the Science Research Council and by the advice and encouragement of his supervisor Dr. Robin Gandy.
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Kranakis, E., Phillips, I. (1984). Partitions and homogeneous sets for admissible ordinals. In: Müller, G.H., Richter, M.M. (eds) Models and Sets. Lecture Notes in Mathematics, vol 1103. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0099389
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DOI: https://doi.org/10.1007/BFb0099389
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