# Predictor subset of another predictor in linear regression model

I have a linear regression model such as $Income_i = \alpha + \beta_1 Primary_i + \beta_2 Secondary_i + \beta_3 Tertiary_i + u_i$ where my predictors $Primary, Secondary, Tertiary$ are dummy variables to indicate the education level. Of course those who have completed tertiary education also completed secondary and primary.

If it's correct to build such a model, then how should I interpret the coefficients and the corresponding $p$-values? Or instead would it be more appropriate to recode the variable $Primary$ so to exclude those who have completed also higher levels of education?