  Investigating the structure of pseudocomplemented lattices started ninety
years ago with papers by V. Glivenko, G. Birkhoff and O. Frink and this
structure was essentially developed by G. Gr\"atzer. In recent years, some
special filters in pseudocomplemented and Stone lattices have been studied by
M. Sambasiva Rao. However, in some applications, in particular in non-classical
logics with unsharp logical connectives, pseudocomplemented posets instead of
lattices are used. This motivated us to develop an algebraic theory of
pseudocomplemented posets, i.e. we derive identities and inequalities holding
in such posets and we use them in order to characterize the so-called Stone
posets. Then we adopt several concepts of special filters and we investigate
their properties in pseudocomplemented posets. Moreover, we show how properties
of these filters influence algebraic properties of the underlying
pseudocomplemented posets.
