You were close:

`word_type + point + gender + (1|speaker/item/repetition)`

This translates to: `repetition` nested in `item`, nested in `speaker`. 

For learning more on lme4 formulas check the [in press paper by Bates et al.][1] (published here as a vignette for lme4), [this answer][2] or [this one][3].


  [1]: http://cran.r-project.org/web/packages/lme4/vignettes/lmer.pdf
  [2]: http://stats.stackexchange.com/questions/70556/have-i-correctly-specified-my-model-in-lmer
  [3]: http://stats.stackexchange.com/a/13173/35989