# What is the "True" population model in linear regression? [duplicate]

What do we mean by a true population model when talking about linear regression? Say I want to study the effects of years of schooling $$S$$ on wages. I posit the following two models:

$$log(wage) = \beta_0 + \beta_1 S + \varepsilon$$

$$log(wage) = v_0 + v_1 S + v_2 A + v$$

where $$A$$ is ability. Which is the "true" population model and what exactly are the requirements for a model to be a "true" model? I know that in this case $$v_1=\beta_1$$ because both measure partial effects of $$S$$ on $$log(wages)$$.

1. Must the "true" population model satisfy the classical regression model assumptions (i.e. zero conditional mean $$E[\varepsilon|S,A] = 0$$ etc?
2. Must the true model simply posit the "correct" functional form relationship between the variables of interest? (i.e. that the true population model must be linear or non-linear)
3. If $$log(wage) = \beta_0 + \beta_1 S + \varepsilon$$ is the "true" population model, if I split $$\beta_1 = l_1 + g_1$$ and rewrite the "true" population model as follows: $$log(wage)=\beta_0+l_1S+e$$ where $$e=\varepsilon+g_1S$$. Is this new model also a "true" population model?

I ask because many econometrics textbooks (especially Wooldridge) introduce a regression model and say that it is a "true" model but never clearly define what exactly constitutes a "true" population regression model.