Gemara

Question (Rav Chananyah): Does the Isur of Techumim apply more than 10 Tefachim above the ground?

We do not ask about [walking on] a pillar 10 tall and four wide. It is [proper to walk on,] like the ground. Surely Techumim apply on top of it!

We ask about a pillar 10 tall and less than four wide;

Version #1: We also ask about flying [using Hash-m's name].

Version #2: We also ask about going in a boat.

Answer #1 (Mishnah): Once, the boat did not enter the port until Shabbos [...R. Gamliel permitted to get off, for it was within the Techum before dark].

If Techumim do not apply above 10, it would be permitted to get off even if it was not in the Techum before dark!

Rejection (Rava): The case is, the boat was in water less than 10 Tefachim deep.

Answer #2 (Beraisa): If one said 'I will be a Nazir on the day that Mashi'ach will come', he may drink wine on Shabbos and Yom Tov, but he is forbidden on weekdays.

If Techumim apply above 10, we understand this. (Mashi'ach cannot come on Shabbos or Yom Tov.) However, if it does not apply, also Shabbos and Yom Tov should be forbidden!

Rejection: Eliyahu will come "Lifnei Bo Yom Hash-m" (the day before), and we know [from tradition] that Eliyahu will not come on Erev Shabbos or Yom Tov, lest this disturb preparations [for Shabbos or Yom Tov].

Answer #3: The Beraisa shows that Techumim do not apply above 10!

If they applied, Eliyahu could not come on Shabbos, so Sunday would be permitted!

Rejection: The Tana is unsure whether or not they apply. Therefore he is stringent. (If it does not apply, Eliyahu could come on Shabbos, and Mashi'ach could come on Sunday.)

Rishonim

Rif (Shabbos 7b): A Beraisa forbids embarking on a boat three days before Shabbos when the water is less than 10 Tefachim deep, due to Techumim.

Rambam (Hilchos Shabbos 27:3): One who walks outside the Techum above 10 Tefachim, e.g. he jumped on pillars 10 Tefachim tall, and each is less than four by four [Tefachim wide], it is a Safek whether or not Techumim apply above 10. If he walks on a place four by four, this is like on the ground, and Techumim apply.

Magid Mishneh: The Rambam said that it is a Safek, but he did not explain how we rule. In a Teshuvah, he explained that we are stringent only when it is a Safek Torah. All Techumim in seas, rivers and Karmelis are mid'Rabanan.

Rosh (4:3): The question of Techumim above 10 Tefachim was not settled. We are stringent.

Hagahos Ashri: Also Mahari'ach is stringent. Or Zaru'a rules that Techumim do not apply above 10, since we hold that Techumim are mid'Rabanan.

Rashi (43b DH b'Chad): Since the Tana forbids drinking on Sunday, we derive that he is concerned lest Eliyahu come, for Techumim do not apply above 10. We reject this. Perhaps the Tana is unsure, and he is stringent to forbid Sunday due to Safek.

Poskim

Shulchan Aruch (OC 404:1): One who walks outside the Techum above 10, e.g. he jumped on pillars 10 Tefachim tall, and each is less than four by four [Tefachim wide], it is a Safek whether or not Techumim apply above 10. We are lenient about a Safek mid'Rabanan.

Beis Yosef (DH Yesh): The Rosh and Hagahos Maimoniyos (30:40, citing Maharam) are stringent about the Safek. This is astounding. Within 12 Mil is a Safek mid'Rabanan, and according to the Rosh, even outside 12 Mil! Also R. Yerucham was astounded at the Rosh. He says that the Rif (Shabbos 7b) connotes that we are lenient, and so holds the Ramban, Rashba and Hagahos Ashri citing Or Zaru'a. Perhaps the stringent opinions learn from the Tana who was stringent due to Safek. The Ritva says that Rashi connotes that we are stringent for this reason. The Ritva says that perhaps we are stringent about Safek Nezirus, for it is mid'Oraisa, but we are lenient about Safek Techumim, for it is mid'Rabanan. Also the Ramban said so.

Mishnah Berurah (1): There is a Safek about Techumim above 10, for is not a [normal] place to walk. People walk primarily on the ground, or at least within 10.

Kaf ha'Chayim (5,6): There is no concern for work with animals regarding trains, and they are primarily for Nochrim and there are fixed departure times. However, even though they are 10 tall, since they are four by four, this is like the ground, and the Isur Techumim apply to them (Tif'eres Yisrael and several others). It is forbidden even if he was in the train from before Shabbos (Chasam Sofer 6:97). Some forbid even within the Techum, due to Uvda d'Chol, or because they burn more fuel when there are more passengers.

Mishnah Berurah (3): If even one pillar is four by four wide and part is outside the Techum, one may not go on that part of it.

Mishnah Berurah (4): If the pillar is less than four wide, even if it is very long, it is inconvenient, so the Safek applies to it.

Rema: However, if he went like this outside of 12 Mil, we are stringent according to the opinion that Techumim of 12 Mil is mid'Oraisa.

Magen Avraham (1): It is mid'Oraisa only for the person. For his Kelim and animal, it is mid'Rabanan (Ralbach). It seems that Maharam Alashkar (41) disagrees.

Maharam Alashkar (41): We say in Beitzah (37a) that one may take an animal or Kli only where its owner could go. Even so, one may give animals to a shepherd, without concern lest he take them outside the Techum. Even the Rambam, who holds that Techumim are mid'Oraisa, says so only for 12 Mil, but not for 2000 Amos. It is not common at all to go 12 Mil. Most Meforshim hold that Techumim is never mid'Oraisa.

Maharam Alashkar (108): The Rashba says that we are lenient about a Safek Techumim, like every Safek mid'Rabanan.

Gra (DH u'Mah): In many places in the Gemara says that we are lenient about a Safek mid'Rabanan, even regarding a Safek whom the Halachah follows, like it says in Avodah Zarah (7a).

Shulchan Aruch (ibid.): Since all agree that there is no Torah Isur of Techumim in seas and rivers, for they are unlike the encampment in the Midbar, [we are lenient about the Safek]. One who was on a boat when Shabbos came has 2000 Amos from where he [first] came within 10 Tefachim of the ground.

Magen Avraham (2): Maharam Alashkar permits descending from the boat in a ferry, since Techumim on the water is always mid'Rabanan, unless it is a place in which people are stringent. Some forbid a ferry. See Tamim De'im (74), and what I wrote in 339:13.

Magen Avraham (3): Even though the water acquired Shevisah, and it is above 10, all water is considered like one body connected to the ground (Tosfos 45b DH Liknu). If one once went on the land after dark, he acquired Shevisah there [so he may go only 2000 Amos from there].

Gra (DH v'Ho'il): The Rif (Shabbos 7b) forbids embarking even on Sunday where there is an Isur Techumim. We must say that the Heter to be on a boat above 10 Tefachim [on Shabbos] is because Techumim do not apply above 10.

Sha'ar ha'Melech (Hilchos Mikva'os 10:6 Klal 5): The Mishneh l'Melech (Avos ha'Tum'ah 8:5) says that even though Safek mid'Rabanan l'Kula, when there is a Sefek-Sefeka to be stringent, we are stringent. R. Shimshon (Yadayim 2:4) says that we are lenient in such a case, but perhaps this is only for Tum'as Yadayim. The Rambam is lenient even for other Sefekos. The Rosh (Shabbos 2:22) brings from R. Yonah that if one placed an Eruv Bein ha'Shemashos, and it was eaten Bein ha'Shemashos, we are not so lenient to say that he placed the Eruv during the day, and it was eaten at night. If we are not always stringent when there is a Sefek-Sefeka, he should have said simply that we are lenient only when there is only one Safek! However, perhaps we are lenient only when the Sefekos came at different times. We were lenient when the first came, as if it were Vadai Heter, and similar when the second comes. If both Sefekos came at once, perhaps we are stringent. The Magid Mishneh is lenient about two Sefekos, for he permits going in a river if it is a Safek whether the water is 10 Tefachim deep. Even if it is, one opinion forbids Techumim above 10! One cannot refute this proof.

Mishnah Berurah (7): The Mechaber is stringent about the Techum of 12 Mil on the land even above 10, for it is a Safek Torah. The Gra favors those who say that it is always mid'Rabanan.