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WEAK REFLECTION AT THE SUCCESSOR OF A SINGULAR CARDINAL

Published online by Cambridge University Press:  25 March 2003

MIRNA DŽAMONJA  and
SAHARON SHELAH
MIRNA DŽAMONJA
Affiliation:
School of Mathematics, University of East Anglia, Norwich NR4 7TJ, [email protected]
SAHARON SHELAH
Affiliation:
Mathematics Department, Hebrew University of Jerusalem, 91904 Givat Ram, Israel Rutgers University, New Brunswick, NJ 08854-8019, [email protected]
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Abstract

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, Džamonja and Shelah.

Type
Notes and Papers
Information
Journal of the London Mathematical Society , Volume 67 , Issue 1 , February 2003 , pp. 1 - 15
Copyright
The London Mathematical Society, 2003

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