Prestige Classes and CL modification

[SeraphX2]

So I am working on my Pathfinder Character Sheet website (shameless link) and I have come across a question I want to clarify about Prestige classes and which Spell Types (Arcane/Divine) they can modify and also how many classes they can modify.

First, the text on Prestige classes seems to state: "in a spellcasting class she belonged to before adding the prestige class".
So this means that it can only be applied to a single class (even if a character is a Mage and a Cleric and the Prestige Class could modify both Arcane and Divine), and that class had to exist before the Prestige class was taken?

Example: A caster is Sorcerer and Mage, and picks up Eldritch Knight; the bonus can only apply to one or the other (even if the criteria are met in both classes)?

Now, concerning CL type, here are my assumptions, based on book text (some will be obvious, but I am listing them all regardless. an (*) denotes the ones I am questioning for sure):

• Arcane Archer: Arcane Only
  
• Arcane Trickster *: Arcane or Divine(?): it seems like it would only be Arcane, but the book text does not specify like Arcane Archer does.
  
• Dragon Disciple: Arcane Only
  
• Eldritch Knight: Arcane Only
  
• Loremaster *: Arcane or Divine: the book text does not specify Arcane or Divine
  
• Mystic Theurge: Arcane or Divine
  

Validations for my theories would be most appreciated. Thanks :)

[Xaratherus]

Correct on everything but Mystic Theurge; it grants spells per day for an arcane class and a divine class.

Mystic Theurge - Spells per Day:

Spells per Day: When a new mystic theurge level is gained, the character gains new spells per day as if he had also gained a level in any one arcane spellcasting class he belonged to before he added the prestige class and any one divine spellcasting class he belonged to previously. He does not, however, gain other benefits a character of that class would have gained. This essentially means that he adds the level of mystic theurge to the level of whatever other arcane spellcasting class and divine spellcasting class the character has, then determines spells per day, spells known, and caster level accordingly. If a character had more than one arcane spellcasting class or more than one divine spellcasting class before he became a mystic theurge, he must decide to which class he adds each level of mystic theurge for the purpose of determining spells per day.

[SeraphX2]

Xaratherus wrote:

Correct on everything but Mystic Theurge; it grants spells per day for an arcane class and a divine class.

** spoiler omitted **

Thanks :)

[Are]

Also note that you can, if you wish, add to one spellcasting class for PrC level 1, and add to another spellcasting class for PrC level 2 (and so on).

Usually, though, unless the PrC advances two classes, it would be best to focus on a single spellcasting class to advance.