Gemara

81b (R. Yosi b'Rebbi Chanina): If Levi picked Bikurim and sent them to Yerushalayim with a Shali'ach, and the Shali'ach died, Levi brings them without reciting. "V'Lokachta... v'Heveisi" - the same person must take and bring them.

Question (Rav Acha brei d'Rav Avya): Why doesn't he say the declaration? Even if they are not Bikurim, he merely recites verses!

Megilah 23b (Mishnah): At least 10 men are required to be Pores Al Shema (to say Kaddish, Borechu, and the first Berachah before Kri'as Shema).

Berachos 21b (Rav Huna): If one entered a Beis ha'Keneses where people are praying, he may begin only if he will finish before the Shali'ach Tzibur (in Chazaras ha'Shatz, i.e. the repitition of Shemoneh Esreh) will reach Modim;

(R. Yehoshua ben Levi): He may begin if he will finish before the Shali'ach Tzibur reaches Kedushah.

Rav Huna holds that an individual says Kedushah (therefore, he need not say it with the Tzibur). R. Yehoshua ben Levi disagrees.

(Rav Ada bar Ahavah): An individual does not say Kedushah, for it says "v'Nikdashti b'Soch Benei Yisrael" -- every matter of Kedushah needs 10.

Rishonim

Rambam (Hilchos Tefilah 7:17): One skips Kedushas Yotzer (i.e. in the first Berachah of Kri'as Shema), for an individual does not say Kedushah.

Hagahos Maimoniyos (90): Rashi, Avi ha'Ezri and my Rebbi permit, for he merely arranges (the angels' praise). Some do not want to say it or skip it, so they say 'Onim v'Omrim b'Yir'ah Kadosh u'Baruch.' La'Kel...'

Rosh (Berachos 3:18 b'Sof): R. Yehoshua ben Levi and R. Yitzchak (our text - Rav Ada) hold that an individual may not say Kedushah (in Chazaras ha'Shatz). However, he may say "Kadosh" in Kedushah d'Sidra (in u'Vo l'Tziyon), for he is like one who says a verse and translates it. Some say that an individual may not say Kedushas Yotzer, he says only 'v'Omrim b'Yir'ah Kadosh u'Baruch.' Some say that an individual may say it. I agree, for we merely a recount how the angels sanctify. One may not say 'Nakdishcha v'Na'aritzcha (we will sanctify and extol You) like the angels do' with less than 10.

R. Yonah (Berachos 13a DH v'Nikdashti): Meforshim argue about whether an individual may say Kedushas Yotzer. Some include this in 'every matter of Kedushah needs 10.' When one reaches 'b'Safah Berurah', he skips it. Chachamim of France and some Ge'onim permit an individual to say it. Only matters like 'Nakdishcha', in which we sanctify Hash-m, require 10. In Kedushas Yotzer, we merely mention what His servants say. U'Vo l'Tziyon is not a problem, for we merely say verses. My Rebbi says like this. Surely, Kri'as Shema is included in 'matters of Kedushah'. Accepting the yoke of Heaven is the ultimate matter of Kedushah! Even so, an individual may say it. The Mishnah requires 10 only to what was initially enacted to say it with 10 due to Kedushah. It was not enacted to say Shema only with 10. The same applies to Kedushas Yotzer, unlike the Kedushah of Na'aritzcha. In every text of Tefilah we find Kedushas Yotzer in the text for an individual, but we do not find Nakdishcha in the text for an individual. This shows that only the latter was enacted to be said (only) with 10.

Rosh (Megilah 3:7 b'Sof): An individual may say Kedushas Yotzer, for it merely recounts how the angels sanctify, like reading verses in Yeshayah. Ten are needed for Kedushah Chazaras ha'Shatz, in which we say 'Nekadesh.'

Teshuvas Rashba (1:7): In a Teshuvah (Blau 313; in other editions 12 or 81), the Rambam says that an individual says this like the Shali'ach Tzibur. Some Ge'onim said oppositely. They hold that it just recounts what the angels say. Kedushah for an individual is to intend to sanctify, like a Shali'ach Tzibur says 'Nekadesh.' Rishonim argued about this. What the Rambam wrote in Mishnah Torah is primary. We learn from "v'Nikdashti b'Soch Benei Yisrael." Rav Huna and R. Yehoshua ben Levi argue about this. A Mishnah requires a Minyan to be Pores Al Shema! Rav Huna explains that is only when one will be Motzi others, like Kri'as ha'Torah and the Haftorah, which that Mishnah mentions. R. Yehoshua ben Levi requires 10 even if one is not Motzi others. They argue about all Kedushos. The Halachah follows R. Yehoshua ben Levi even against R. Yochanan, all the more so against Rav, or Rav's Talmid Rav Huna. Also, Rav Ada holds like R. Yehoshua ben Levi. They are a majority against Rav Huna. We do not rely on Maseches Sofrim (which permits) against our Gemara. Gedolim say that in Kedushas Yotzer we merely say what the angels say, so one may say it with the cantillation. We do not say it at all. In such matters, it is proper to be passive and refrain.

Poskim

Shulchan Aruch (OC 59:3): Some say that an individual may say Kedushas Yotzer, for it is merely a recount. Some say that an individual skips it, and it is said only b'Tzibur. One should be concerned for their opinion, and an individual should be sure to say it with the cantillation like one who reads verses.

Beis Yosef (DH Kedushah): R. Yerucham and Mahari Avuhav say that the Rambam's son said that the Rambam retracted in a Teshuvah, and concluded like the Rosh who permits an individual to say it. The Kolbo (8) says that since the Rambam wrote so in a Teshuvah, but not in the Mishnah Torah, he holds that this is the Halachah, but we do not openly rule like this. Orchos Chayim says that we rely on the Rambam's son that he retracted and said that we openly rule like this.

Beis Yosef (DH b'Perek): The Ran (Megilah 13b DH v'Sham'inan) learns from there that an individual does not say Kedushas Yotzer, but he may say Kedushah d'Sidra, for it is mere verses. R. Yerucham, the Manhig and Rav Natrunai Gaon agree. Shibolei ha'Leket says that that R. Eliezer of Virona says that we say 'Omrim b'Yir'ah Kadosh u'Baruch." R. Baruch disagrees, for different angels say 'Baruch'! Rather, he says 'Omrim b'Yir'ah Kadosh... veha'Ofanim... Omrim Baruch', but he does not finish the verses. This is primary.

Beis Yosef (DH v'Chosav): The Tur says that Maseches Sofrim permits an individual to say Kedushas Yotzer and Kedushah d'Sidra. Mahari Avuhav says that it permits only an adult. The custom is like R. Yonah and the Rosh, who permit even minors. However, the Zohar forbids an individual to say Kedushas Yotzer and the Lashon ha'Kodesh in Kedushah d'Sidra. We learn from it that we say the Targum (in u'Vo l'Tziyon) quietly, for we do not say things in Aramaic b'Tzibur. Therefore, every individual says it himself. The custom is for individuals to say Kedushas Yotzer. I say that since it is not explicit in the Gemara, we should follow the Zohar.

Darchei Moshe (3): We rely on the Rambam's retraction in the Teshuvah, R. Yonah and the Rosh. We are not concerned for the Zohar against our custom, which is based on what is explicit in Maseches Sofrim.

Rebuttal (Gra 5): Maseches Sofrim (16:12) requires 10 also to be Pores Shema, just it suffices if six or seven did not hear it yet.

Kaf ha'Chayim (21): For Kedushas Yotzer or Kedushah d'Sidra, we are not concerned if three or four of the 10 lag behind and do not say it with the Tzibur. For Kedushah of Chazaras ha'Shatz, nine must be listening to the Shali'ach Tzibur.

Beis Yosef (DH uv'Sefer): Sefer ha'Pardes cites a Ga'on who forbids an individual to say Kedushah d'Sidra. Rather, a Chacham learns a teaching of praise, such as 'three kinds of angels sing Shirah every day.' If he is not a Chacham, he learns verses with Kedushah d'Sidra, such as "Serafim stand." Some say that since they are verses, an individual says them with the cantillation. Terumas ha'Deshen (8) says that an individual says these Kedushos with the cantillation, and all permit this. It is proper to do so.

Gra (5): Surely, Megilah 23b requires 10 for Birkas Yozter due to the Kedushah. The Beis Yosef (69 DH Tanan) and Darchei Moshe (69:1) give an alternative answer (10 are needed to be Motzi others), but this is very weak.

Mishnah Berurah (3): All agree that one may say it amidst a Tzibur, even if he prays alone because he came late.

Kaf ha'Chayim (21): Ma'amar Mordechai disagrees.

Mishnah Berurah (11): One should be stringent like the Gra to say it with the cantillation when he is not in a Tzibur.

Kaf ha'Chayim (22): It is good to always say it with the cantillation, so he will be used to this for when he is not in a Tzibur. The Ari Zal says to say all verses in prayer with the cantillation.

Rema: The custom has spread like the first opinion.

Rema (132:1): The law of an individual saying Kedushah d'Sidra is like the law of Kedushas Yotzer. See Siman 59.

Mishnah Berurah (3): One should try to say it with the Tzibur. If he lags behind the Tzibur, he says it with them, and afterwards Ashrei and Lamnatze'ach and the two verses before the Kedushah.

Kaf ha'Chayim (8): According to the Ari Zal, it must be said after Ashrei and Lamnatze'ach. One may say it alone with the cantillation.

Tur (621:5): In the Avodah on Yom Kipur, Rav Sadya Gaon says that we say 'Lifnei ha'Shem' and 'Ana ha'Shem' (just like this). The Ritz Ge'as says that there is no problem if one said "Lifnei Hash-m" (i.e. Aleph-Dalet, the way we say in Berachos), for he reads a verse and does not pronounce Hash-m's name like it is written.

Bach (5): I say that Rav Sadya Gaon holds that since we merely recount what was done, but we do not request or praise Hash-m, if one says His name it is Levatalah. The Ritz Ge'as is lenient only about "Lifnei Hash-m", for it is a verse. One may say it 1000 times in a day! In Bava Basra we permit to recite for Bikurim mi'Safek, for he says verses.

Taz (2): In Kedushas Yotzer we say "Hash-m", even though we merely recount the angels' praise, for it is verses.