20 research outputs found
On complete representability of Pinter's algebras and related structures
We answer an implicit question of Ian Hodkinson's. We show that atomic
Pinters algebras may not be completely representable, however the class of
completely representable Pinters algebras is elementary and finitely
axiomatizable. We obtain analagous results for infinite dimensions (replacing
finite axiomatizability by finite schema axiomatizability). We show that the
class of subdirect products of set algebras is a canonical variety that is
locally finite only for finite dimensions, and has the superamalgamation
property; the latter for all dimensions. However, the algebras we deal with are
expansions of Pinter algebras with substitutions corresponding to
tranpositions. It is true that this makes the a lot of the problems addressed
harder, but this is an acet, not a liability. Futhermore, the results for
Pinter's algebras readily follow by just discarding the substitution operations
corresponding to transpostions. Finally, we show that the multi-dimensional
modal logic corresponding to finite dimensional algebras have an -complete
satisfiability problem.Comment: arXiv admin note: substantial text overlap with arXiv:1302.304