We provide a short proof that if κ is a regular cardinal with κ < c, then
![](//static-cambridge-org.ezproxyberklee.flo.org/content/id/urn%3Acambridge.org%3Aid%3Aarticle%3AS002248120000428X/resource/name/S002248120000428X_Uequ1.gif?pub-status=live)
for any ordinal α < min{
, κ}. In particular,
![](//static-cambridge-org.ezproxyberklee.flo.org/content/id/urn%3Acambridge.org%3Aid%3Aarticle%3AS002248120000428X/resource/name/S002248120000428X_Uequ2.gif?pub-status=live)
for any ordinal α <
. This generalizes an unpublished result of E. Szemerédi that Martin's axiom implies that
![](//static-cambridge-org.ezproxyberklee.flo.org/content/id/urn%3Acambridge.org%3Aid%3Aarticle%3AS002248120000428X/resource/name/S002248120000428X_Uequ3.gif?pub-status=live)
for any cardinal κ with κ < c.