Combinatorics of dense subsets of the rationals

Abstract

We study combinatorial properties of the partial order $({\rm Dense}(\Bbb Q ), \subseteq)$. To do that we introduce cardinal invariants $\frak p_\Bbb Q,\frak t_\Bbb Q,\frak h_\Bbb Q,\frak s_\Bbb Q,\frak r_\Bbb Q, \frak i_\Bbb Q$ describing properties of $