R help - Jul 2007 - DF and intercept term meaning for mixed (lme) models

Hi,

I am using the lme package to fit mixed effects models to a set of data.

I am having a difficult time understanding the *meaning* of the numDF (degrees 
of freedom in the numerator), denDF (DF in the denomenator), as well as the 
Intercept term in the output.

For example:

I have a groupedData object called 'Soil', and am fitting an lme model
as
follows:

## fit a simple model
# errors partitioned among replicates
fit1 <- lme(
? ?log(ksat) ~ log(conc) + ordered(sar) + soil_id ,
? ?random = ~ 1 | rep,
? ?data=Soil
)

## check significance of model terms
anova(fit1)

? ? ? ? ? ? ? numDF denDF ?F-value p-value
(Intercept) ? ? ?1 ?1253 64313.21 ?<.0001
log(conc) ? ? ? ?1 ? 597 ? 173.34 ?<.0001
ordered(sar) ? ? 2 ? 597 ? ?13.87 ?<.0001
soil_id ? ? ? ? 29 ? 597 ? ?54.92 ?<.0001


I am pretty sure that I am interpreting the p-values for the predictor terms 
to mean that these terms contribute significantly to the variation in the 
response variable, (?) . I am not sure what the significance of the Intercept 
term really means. Does it have something to do with the significance of the 
random effects in the model?

Also, from a practical standpoint, how can I best describe / interpret the 
numDF and denDF terms to others... or do they even matter to a person who is 
looking to see if the 'treatment' predictor terms had any effect on the 
response term?

Thanks in advance. 

Dylan