Gemara

32b (Mishnah): If an Eruv was in a tree above 10 Tefachim, it is invalid;

If it is below 10 Tefachim, it is valid;

The tree is in Reshus ha'Rabim. He intended his Shevisah to be on the ground. The Isur to use a tree is mid'Rabanan. Our Mishnah is Rebbi, who permits Shevus during Bein ha'Shemashos.

34b (Mishnah): If one was Me'arev in a cabinet and lost the key, even so it is valid;

R. Eliezer says, if he does not know where the key is, it is invalid.

35a (Abaye and Rava): The case is, the lock is tied with ropes, and a knife is needed to break them. The first Tana holds like R. Yosi, who permits moving [almost any] Kli on Shabbos;

R. Eliezer holds like R. Nechemyah, who says that a Kli may be moved only for its intended purpose.

36a (Mishnah): If a Tevul Yom flask (it was immersed today) was filled with Ma'aser that is Tevel [to Terumas Ma'aser], and the owner said 'it should be Terumas Ma'aser at dark', this takes effect. If he was Me'arev with it, it is invalid.

Yevamos 93a: R. Yanai's sharecropper used to bring to him Peros every Erev Shabbos. Once he delayed coming. R. Yanai took Ma'aser from his own fruits on the fruit he expected to receive.

Rishonim

Bartenura (Eruvin 3:3): Cutting rope is Shevus. R. Eliezer holds like R. Nechemyah, who permits moving a Kli only for its intended purpose. Since one must transgress two Shevusim in order to get the Eruv, even Rebbi forbids Bein ha'Shemashos.

Tosfos (35a DH Bo'i): Rashi says that if he could untie it by hand, even R. Eliezer is Machshir, for it is Mekalkel. The Isur is only mid'Rabanan, for it looks like Binyan and Stirah, so it is permitted Bein ha'Shemashos. This is wrong. Even if R. Eliezer holds like R. Nechemyah, the Isur to move a knife is only mid'Rabanan! Rather, the cabinet is a Kli. If he can untie it by hand, R. Eliezer totally permits. He forbids if he needs a knife. He holds like R. Nechemyah, and he forbids Shevus Bein ha'Shemashos, unlike Rebbi.

Terumas ha'Deshen (269): If Pidyon ha'Ben (day 31) falls on Shabbos, we do not redeem on Shabbos with a Kli, for this is like business. To redeem before and stipulate is difficult. How can one bless or make the customary Seudah, which some say is a Seudas Mitzvah?!

Hagahos Maimoniyos (Hilchos Shabbos 6:2): One may not give money to a Nochri before Shabbos for him to buy in the market on Shabbos, for we are stringent to say that Shelichus applies to Nochrim.

Poskim

Shulchan Aruch (YD 305:11): If the 31st day from the birth of a Bechor is on Shabbos, we do not redeem him until Sunday.

Magen Avraham (339:8): One cannot give the money before Shabbos, for there is no solution for the Berachos and the meal. Before Shabbos, he cannot say "v'Tzivanu (You commanded us)." He cannot bless on Shabbos, for he does not do anything now (Terumas ha'Deshen).

Question: If on Erev Shabbos one sold an item through Meshichah or Kesef, may he stipulate that the Kinyan take effect on Shabbos? Or, if there was a Tanai (stipulation) to be fulfilled later, may one do an action on Shabbos to fulfill the Tanai? Perhaps we permit both. In the first case, he does no action on Shabbos. The Kinyan finishes by itself. This is permitted. In the latter case, even though he doing an action, it is mere Kiyum (fulfillment) of the Tanai. The Kinyan is completed retroactively on Erev Shabbos. Or, perhaps both are forbidden. In the first case, the final Kinyan is on Shabbos. In the latter case, his action of Kiyum ha'Tanai finalizes the Kinyan. Or, perhaps one of these is permitted, and the other is forbidden!

Answer (R. Akiva Eiger 1:159): It seems that we can answer the first question from the Terumas ha'Deshen, who forbids redeeming on Shabbos. We do not say to give the money to the Kohen before Shabbos, due to the Berachos and Seudah. If not for this, it would be permitted. We need a better proof from the Gemara.

Question (Sha'agas Aryeh 93): R. Yehudah (Yoma 13b) holds that the Kohen Gadol marries a second wife, and divorces both wives before Yom Kipur. He stipulates that one is divorced if her co-wife will not die on Yom Kipur, and the other is divorced on condition that he enter the Beis ha'Keneses. Why must he marry and divorce? He could be Mekadesh "after my current wife will die." The moment she dies, the other Kidushin takes effect!

Answer (R. Akiva Eiger ibid.): It is Shevus (Asur mid'Rabanan) to make a Kidushin that will take effect on Yom Kipur. Even though Ein Shevus b'Mikdash [if this would hinder Avodah], when there is another solution, this is better. If so, we must say that one may not stipulate for a Kinyan to take effect on Shabbos, but one may fulfill a Tanai on Shabbos. In the method used, the Kohen Gadol fulfills the Tanai on Yom Kipur. If the first case (stipulating to take effect on Yom Kipur) were not more stringent, it would have been better [to avoid a needless Kidushin and divorce].

Question: Why wasn't he Mekadesh "on condition that I enter the Beis ha'Keneses", and divorce his current wife "on condition that I do not enter"? If his current wife dies, he will enter!

R. Akiva Eiger (DH v'Nir'eh): The Bartenura says that all forbid two Shevusim Bein ha'Shemashos. In Eruvin 32b we are Machshir an Eruv in a tree, even though to get it he must transfer from Karmelis to Reshus ha'Rabim, and use a tree! Even ha'Ozer answered that the stringency is only when two Shevusim come together. This is forbidden even in the Mikdash. Therefore, the Kohen Gadol was not Mekadesh on Tanai, for by doing an action to make the divorce [of his first wife] take effect, at the same time he causes the Kidushin to take effect, which is a second Shevus. We can say even simpler, that it is bring to minimize Shevus. Through Kidushin before Yom Kipur and divorce on Yom Kipur, he causes only one Shevus.

Note: This is a big Chidush. Surely, it was a small minority of years that his wife died. In most years, Kidushin on Tanai would avoid the need to transgress any Shevus, and to disqualify a girl from Kehunah!

R. Akiva Eiger: We must say that stipulating to take effect on Shabbos is Shevus, and also fulfilling the Tanai. If not, he should be Mekadesh and do Chupah on condition to take effect after his current wife dies, or on condition that he enter the Beis ha'Keneses!

Igros Moshe (OC 3 44): R. Akiva Eiger brought a proof from the Terumas ha'Deshen and Magen Avraham, to permit a Kinyan before Shabbos that will take effect on Shabbos. R. Akiva Eiger concluded that it is forbidden. He did not say that he argues with them, and it is difficult to rely on a proof against them. He learned from the Bartenura that two Shevusim are forbidden Bein ha'Shemashos. Tosfos (35a) does not distinguish. He must have another answer to explain Yoma 13b! Tosfos (13b DH ul'Chada) says that the Yerushalmi says that R. Yehudah holds that he was not Mekadesh a second wife, just they prepared a girl. If his wife would die, he would be Mekadesh her on Yom Kipur. Even though this is Shevus, it is permitted in the Mikdash. If one may make a Kinyan to take effect on Shabbos, why wasn't he Mekadesh her from before Yom Kipur, to take effect after his wife will die?

Chazon Ish (Demai 9:12 DH ha'Gaon): According to R. Akiva Eiger, we must say that the Heter to make Terumah take effect at night [on Shabbos - 36a], and R. Yanai's separation (93a) are due to the Heter of a Tanai. Just like a Tanai works, it permits to make it take effect on Shabbos or fulfill the Tanai on Shabbos. (R. Akiva Eiger forbids stipulating using Breirah that it take effect on Shabbos.) R. Shimshon (Demai 4:4) says that R. Yanai separated before he knew that a Tanai helps for Vadai Tevel. He holds that even without a Tanai, one may stipulate that it take effect on Shabbos, like the Terumas ha'Deshen.

Igros Moshe (OC 3:44): There is not such a proof from Terumas ha'Deshen. The Gemara did not say that we do not redeem on Shabbos. The Rivash (156) said so. Pidyon ha'Ben is not like other redemptions, in which the Kedushah goes onto the money, or like Pidyon Peter Chamor, which permits the donkey. It merely sounds like buying and selling. It is a gift for the sake of a Mitzvah that should be done today. The proofs of the Terumas ha'Deshen and R. Akiva Eiger are not solid. One should be stringent about a Safek, especially since R. Akiva Eiger rules like this.

Igros Moshe: One may not tell a stock broker on a weekday to buy when the stock reaches a certain price. The Nochri sells for the Yisrael on Shabbos or Yom Tov, due to his command. OC 307:4 explicitly forbids telling a Nochri to buy, and likewise one may not tell him to sell. Even if he makes the broker an agent to buy or sell also during the week when the stock reaches a certain price, the Nochri is obligated to do so also on Shabbos, so it is forbidden. This is unlike making a Shali'ach to buy [Stam], for then he need not buy on Shabbos. One may sell to the Nochri broker on Shabbos on condition that it will be worth a certain amount on Shabbos. Even R. Akiva Eiger permits, for it takes effect on Erev Shabbos, and he does no action on Shabbos.