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names of model coefficients etc

I am curious about the reason for the following:
[1] "(Intercept)"  "x"            "cbind(z, w)z" "cbind(z, w)w"
[1] "y"             "x"             "cbind(z, w).z" "cbind(z, w).w"
[1] FALSE  TRUE FALSE FALSE

It would be helpful for some purposes if all components except the 
first here could be TRUE.  Presumably there is some good reason for 
the difference?  Can someone please enlighten me?