Article history: Received 8 April 2008 Received in revised form 14 May 2008 Accepted 27 June 2008 Available online 5 July 2008 PACS: 61.50.-f 71.15.Mb 71.27.+a

We show that it is consistent that the product of perfectly meager sets is perfectly meager.

We list the subgroups of the basis set of Cl3,0 and classify them according to three criteria for construction of universal Clifford algebras: (1) each generator squares to ±1, (2) the generators within the group anticommute, and (3) the order of the resulting group is 2, where n is the number of nontrivial generators. Obedient groups we call choirs; disobedient groups, bands. We classify choir...