Do PrC caster levels stack?

Apologies if this is a FAQ, but even with the search function I couldn't find the answer here.

Suppose you are a Wizard, and you take some levels of a PrC that grants "+1 level of existing class". For example, the Loremaster. Now this PrC explicity states: "This essentially means that she adds the level of loremaster to the level of some other spellcasting class the character has, then determines spells per day, spells known, and caster level accordingly."

http://www.opengamingfoundation.org/srd/srdbasiccharacterclassesi.rtf

Do all PrCs that add "+1 level of existing class" function similar vis-a-vis caster level?

What about Mage of the Arcane Order (T&B)? It doesn't mention caster level in the paragraph on Spells per Day (p. 61, 2nd column).

:confused:
 

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