  The effect of annealing at room temperature on the fluctuation conductivity
(FLC) $\sigma^\prime(T)$ and pseudogap (PG) $\Delta^*(T)$ in the basal ab plane
of $ReBa_2Cu_3O_{7-\delta}$ (Re = Ho) single crystals with a lack of oxygen has
been studied. It is shown that at all stages of annealing, the FLC near $T_c$
can be described by the Aslamazov$-$Larkin and Maki$-$Thompson fluctuation
theories, demonstrating a 3D$-$2D crossover with increasing temperature. The
crossover temperature $T_0$ was used to determine the coherence length along
the $c$-axis, $\xi_c(0)$=2.82 A. At the inter-mediate stage of annealing, an
anomalous increase in 2D FLC was revealed, which is associated with the
influence of uncompensated magnetic moments in $HoBa_2Cu_3O_{7-\delta}$
(HoBCO): $\mu_{eff, Ho}$=9.7$\mu_{B}$. For the quenched sample S1, the
temperature dependence of the PG has a shape typical of single crystals with a
large number of defects. However, $\Delta^*(T)$ has two small additional maxima
at high temperature, which is a feature of HoBCO single crystals with
pronounced twins and indicates the two-phase nature of the sample. Upon
annealing, the shape of $\Delta^*(T)$ noticeably changes, very likely due to an
increase in the magnetic interaction (sample S2). More important is the change
in the slope of the data at high temperatures, which has become about 3.5 times
steeper. The ordering of the oxygen distribution due to the diffusion process
during annealing somewhat compensates for the influence of magnetic
interaction. Interestingly, the slope turns out to be the same as for
FeAs-based superconductors, suggesting the possibility of the existence of spin
density waves in HoBCO in the PG state.
