AB4.5

The file ab45.zip, that includes both the dvi and ps version, is now available at ftp.math.mcgill.ca/pub/barr. It is a preliminary version because I want to investigate if the condition is really stronger than AB4. The following consideration raises the possibility that it might not be. One place to look to distinguish AB4* from AB4.5* might be in the abelian groups of a topos. But in order for the abelian groups of a topos to satisfy AB4*, you need AC (in the topos). But AC implies dependent choice and then it looks like you have AB4.5*, which really is just like dependent choice. Michael