Can an Archivist benefit from features that affect spell books, such as Eidetic Spellcaster or Geometer?

Question

Can a multiclass Archivist-Wizard benefit from class features that affect the spellbook class feature?

Class "Archivist" from Heroes of Horror book is a divine class that works mostly like a wizard only with divine spells instead of arcane.

In order to keep a list of available spells, this class uses a Prayerbook, which is described as a Wizard's spellbook, only for divine spells:

Prayerbook: Unlike a cleric, an archivist does not receive his daily spell complement from whatever deity or cosmic force he worships. Rather, he must seek out and collect new spells much as a wizard does, but from such esoteric sources as holy tablets, ancient steles, or other magical scriptures. He cannot prepare any spell not recorded in his prayerbook except for read magic, which archivists can prepare from memory.

An archivist begins play with a prayerbook containing all 0-level cleric spells plus three 1st-level cleric spells of the player's choice. For each point of Intelligence bonus the archivist has, the prayerbook has an additional 1st-level cleric spell. At each new class level, the archivist gains two new cleric spells for his prayerbook; these can be of any spell level or levels that he can cast (based on hisnew archivist level). At any time, an archivist can also add spells found on scrolls containing divine spells to his prayerbook, but he must make any rolls and spend the time required (see Adding Spells to a Wizard's Spellbook on page 178 of the Player's Handbook). The archivist can learn and thus prepare nonclerical divine spells in this fashion but the two free spells he gains for advancing in class level must be selected from the cleric spell list.

Since it is like a spellbook, some stuff that improves spellbook usage should affect the prayerbook as well. Some examples would be:

• Geometer prestige class in Complete Arcane can reduce the number of pages used in a spellbook when writing a spell
• Eidetic Spellcaster alternative class feature allows a Wizard to keep a spellbook in memory instead of in physical form (but still need to spend money per page)
• Spell Mastery feat allows a spellcaster to cast certain spells as if that spell was in the caster's spellbook
• Boccob's Blessed Book is a wondrous item that permits writing spells in it without spending so much money
• Etc.

In my opinion this would follow Rules As Intended (i.e. it functions like a spellbook) and it would not be too overpowered (you are losing levels of one class to get levels from the other one).

Answer 1

Ask your DM

There just is no way to definitively answer this question either way within the rules, for all the reasons you’ve covered in your question: all of these features say “spellbook” while the archivist has a “prayerbook,” but the prayerbook feature equates itself to the spellbook feature in the parenthetical directing you to “see Adding Spells to a Wizard’s Spellbook.” There’s just no way to know exactly how far that goes, and whether or not it would extend to include any of your examples or others.

Neither errata (which doesn’t exist for Heroes of Horror) nor even the FAQ (which has a couple of archivist questions but not this one) helps us here.

So this is fundamentally ambiguous and must be ruled on by a DM. There is no other possible answer to this question.

One thing that we can say for sure is that it does not matter if the character is a multiclass wizard/archivist or a single-classed archivist. Nothing about being a wizard is going to change how the prayerbook works. Either it works with these features, or it does not.