If he said 'Korban, I will not eat from you,' or 'Korban she'Ochel of yours,' or 'Lo Korban, I will not eat from you,' he is permitted. (The first two are Shevu'os in the life of a Korban, which are void. The last case is permitted, for the Tana does not infer 'yes' from 'no' - RAN 16a.)

'Shevu'ah, I will not eat of yours,' 'Shevu'ah she'Ochel of yours,' or 'not a Shevu'ah, I will not eat of yours,' he is forbidden. This is a stringency of Shevuos over Nedarim;

A stringency of Nedarim over Shevuos is that if one said 'Konam Sukah, I will not make one' or similarly regarding Lulav, or Tefilin, he is forbidden. Such a Shevu'ah does not forbid, for one cannot swear to override Mitzvos. (RASHBASH (334) - in the Bavli (16b), Rava says that he swore not to sit in a Sukah, for making a Sukah is merely Hechsher Mitzvah, and the Shevu'ah would take effect.)

(Gemara) Question: Why was it not taught 'Shevu'ah she'Lo Ochel of yours,' he is permitted? (The prefix 'she' switches a Shevu'ah from swearing to do or not do, to forbidding 'that which', so he forbids what he will not eat. Therefore, he may eat.)

Answer #1: Because it was taught a stringency of Shevuos over Nedarim. (This is a leniency of Shevu'os.)

Answer #2: We are thinking that [only R. Yehudah, who permits one who says 'Yerushalayim', is lenient, but] 'Shevu'ah she'Lo Ochel of yours,' Chachamim forbid (they are stringent; perhaps he swears not to eat of his). Therefore, it was not taught. (We explained this like MEICHAL HA'MAYIM.)

Harei it is Korban, Harei it is l'Korban, Harei it is k'Korban - (if he said any of these), he is forbidden. Harei it is Shevu'ah, Harei it is li'Shevu'ah, Harei it is ki'Shevu'ah - (if he said any of these), he is permitted. (Shevu'os do not forbid items.)

This is a stringency of Shevuos over Nedarim. A stringency of Nedarim over Shevuos - ""Oh Nefesh Ki Sishava Levatei bi'Sefasayim Lehara Oh Leheitiv" - just like Leheitiv (doing good) is Reshus (optional), also Lehara. This excludes a matter of Isur and a matter of Mitzvah.

Assumption: This is only if b'Shogeg (he swore to annul or fulfill a Mitzvah), but not b'Mezid (then, it takes effect)!

Rejection: A Beraisa was found in which R. Yishmael says "k'Chol ha'Yotzei mi'Piv Ya'aseh", and not what came out from Shamayim (a Mitzvah or Aveirah).

Suggestion: We should say so even about Hekdesh (it does not take effect on Mitzvos)!

Rejection (R. Yosah citing R. Heila): A person can be Makdish his Sukah to Shamayim. (We explained this like TAL TORAH.)