Some open questions in algebraic logic

Attributions are to the best of my knowledge — corrections welcome, as are solutions.
Below, n denotes a finite integer.
  1. Is RRA axiomatisable in first-order logic with n variables, for any finite n? 
  2. Is SRaCAn (n > 4) closed under completions?
  3. Is RA5 closed under completions?

    4. (For n>5, RAn is not closed under completions.) 
  4. Is there a set of canonical equations axiomatising RRA [Yde Venema]?
  5. Is there a set of canonical equations axiomatising SRaCAn?  Same for RAn. 
  6. It is known that RAn properly contains SRaCAn for each n>4, and that SRaCAn is not finitely axiomatisable over RAn, but that the intersection of all RAn is RRA, which is contained in any given SRaCAn.

    7. Is there a function f:\omega -> \omega such that RAf(n)\subseteq SRaCAn for all n>4?
    Is there a recursive f?
  7. Is every algebra in SRaCAn (n>4) embeddable in a RA with a n-dimensional cylindric basis?

    8. (Not every atomic algebra in SRaCAn has a n-dimensional cylindric basis itself - eg a representable projective-plane-Lyndon algebra with at least 6 atoms has no 5-dimensional cylindric basis; but it clearly embeds in a RA with such a basis.) 
  8. Is the class of atom structures of complex algebras in RRA an elementary class [Roger Maddux 1982]?
 

Ian Hodkinson, July 1998