I was looking through the brachot this morning. Many are structured as identifying hashem as "one who __" such as "matir assurim" or "oteir yisro'el btif'arah." But the final three add in the letter hei before the verb to say "THE one who __" ("hanotein," "hama'avir" and "hagomeil").
Baruch she'amar ends with "melech mehulal" but yishtabach ends with "habocheir b'shirei..."
After borchu, we say "oseh shalom" and "yotzer" but before shma we say "habocheir." [in ma'ariv we say "hama'ariv" but then "oheiv"]
Is there any consistent rule which would help me understand why a bracha might or might not include the letter hei? This is potentially just explainable through a ruling of Hebrew grammar but I sense that there is (should be?) a theological difference between the words.
NOTE -- As source material I used the texts of the Siddur Tefilla Hashaleim (Askenaz and Sefard) - Greenwald, The Siddur Margalit Tovah (Ashkenaz, Eshkol Publishing), The Siddur Chazon Ovadia and some Artscrolls. The Artscrolls have "gomeil" not "hagomeil" and some texts have "asher heichin" instead of "hameichin."