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Similar but not the same: various versions of ♣ do not coincide

Published online by Cambridge University Press:  12 March 2014

Mirna Džamonja
School of Mathematics, University of East Anglia, Norwich, NR4 7TJ, UK, E-mail:
Saharon Shelah
Mathematics Department, Hebrew University of Jerusalem, 91904 Givat Ram, Israel, E-mail:


We consider various versions of the ♣ principle. This principle is a known consequence of ◊. It is well known that ◊ is not sensitive to minor changes in its definition, e.g., changing the guessing requirement form “guessing exactly” to “guessing modulo a finite set”. We show however, that this is not true for ♣. We consider some other variants of ♣ as well.

Research Article
Copyright © Association for Symbolic Logic 1999

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