Unlike Bell's method, Hall's does not use transfinite induction.
To show the greater simplicity of our method over Brown's, let us......
Hörmander's theorem [without “the”] = the Hörmander theorem
a theorem of Hörmander's [= one of Hörmander's theorems]
But we have......, which, by another theorem of Kimney's, is more than enough to guarantee that P gives A outer measure 1.
Gauss's remarkable theorem on...... = the remarkable theorem of Gauss on......
[Adding 's is recommended even after names ending in s, z or x, except ancient ones: Pythagoras' theorem; however, the forms like Jones' theorem are also correct.]
Fefferman and Stein's theorem = the Fefferman--Stein theorem
[In the plural of abbreviations and numerals, the apostrophe is best omitted: five 1s, PDEs, in the 1980s. However, it should sometimes be used to avoid confusion: There are three i's in row k.]