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Journal of the London Mathematical Society 2003 67(1):1-15; doi:10.1112/S0024610702003757
© 2003 by London Mathematical Society
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© The London Mathematical Society

Weak Reflection at the Successor of a Singular Cardinal

Mirna Dzamonja and Saharon Shelah

School of Mathematics, University of East Anglia Norwich NR4 7TJ, m.dzamonja{at}uea.ac.uk
Mathematics Department, Hebrew University of Jerusalem 91904 Givat Ram, Israel
Rutgers University New Brunswick, NJ 08854-8019, USA, shelah{at}sunset.huji.ac.il

Received 14 March 2000. Revision received 1 March 2002.

The notion of stationary reflection is one of the most important notions of combinatorial set theory. Weak reflection, which is, as its name suggests, a weak version of stationary reflection, is investigated. The main result is that modulo a large cardinal assumption close to 2-hugeness, there can be a regular cardinal {kappa} such that the first cardinal weakly reflecting at {kappa} is the successor of a singular cardinal. This answers a question of Cummings, Dzamonja and Shelah.


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