DC with Metamagic and Metamagic Reducers

[bishop]

Question on the DC of spells that you have added metamagic to but also used reducers.

Example:

1. Cast a Fireball as a 5th level Wizard with a 16 Int.
Would the DC be 10 + Spell Level (3) +  Casting Modifier (3) for a DC of 16?

2. Cast an Empowered Fireball as a 5th level Wizard with a 16 Int.
Would the DC be 10 + Spell Level (3+2 [Empowerd]) +  Casting Modifier (3) for a DC of 18?

3. Cast an Empowered Fireball as a 5th level Wizard with a 16 Int and Arcane Thesis (Fireball).
Would the DC be 10 + Spell Level (3 + 2[Empowerd] - 1 [Arcane Thesis]) +  Casting Modifier (3) for a DC of 17?

Basically curious if metamagic reducers reduce the DC of the spell or if it would still be at the same heightened level. Also I am assuming that metamagic does increase the spell level and therefore the DC, please let me know if I am accurate on that as well.

Thank you for all of your help.

[wotmaniac]

No, your base assumption is wrong.  Metamagic feats do not affect the DC of the spell (except for Heighten Spell):

Spells modified by a metamagic feat use a spell slot higher than normal. This does not change the level of the spell, so the DC for saving throws against it does not go up.

emphasis mine.

To further answer your question, if I cast a maximized fireball (6th level slot) as a 15th level wizard, and also heighten that spell to 8th level (+2 heighten), the dc would be 15+stat (10base + 3spell +2 heighten).  Reducers would certainly give you more room to heighten; but that's about it as far as DCs go.

[bishop]

I had forgot about Heighten spell specifically doing that. Thank you very much for the help and reminder.