 For Γ0, a fundamental sequence could be chosen to be formula_32 and formula_33

For Γβ+1, let formula_34 and formula_35

For Γβ where formula_36 is a limit, let formula_37

To build the Veblen function of a finite number of arguments (finitary Veblen function), let the binary function formula_38 be formula_39 as defined above.Let formula_40 be an empty string or a string consisting of one or more comma-separated zeros formula_41 and formula_42 be an empty string or a string consisting of one or more comma-separated ordinals formula_43 with formula_44.The binary function formula_45 can be written as formula_46 where both formula_42 and formula_40 are empty strings.