סימן טו סעיף א
אַחַר יִשְׁתַּבַּח, אוֹמֵר הַשְּׁלִיחַ צִבּוּר חֲצִי קַדִּישׁ. אֵין אוֹמְרִים קַדִּישׁ וּבָרְכוּ וּקְדֻשָּׁה וְאֵין קוֹרִין בַּתּוֹרָה אֶלָּא בַּעֲשָׂרָה אֲנָשִׁים גְּדוֹלִים. וְאִם לֹא הָיוּ עֲשָׂרָה בְּשָׁעָה שֶׁאָמְרוּ יִשְׁתַּבַּח אֶלָּא שֶׁנִּשְׁלְמוּ אַחַר כָּךְ, לֹא יֹאמַר הַשְּׁלִיחַ צִבּוּר קַדִּישׁ, כִּי אֵין אוֹמְרִים קַדִּישׁ אֶלָּא אַחַר דָּבָר שֶׁנֶּאֱמַר בַּעֲשָׂרָה. וְלָכֵן יַמְתִּינוּ מִלּוֹמַר יִשְׁתַּבַּח עַד שֶׁיָּבוֹאוּ עֲשָׂרָה. וִיכוֹלִין לְהַמְתִּין עַד קָרוֹב לַחֲצִי שָׁעָה, וְיוֹתֵר לֹא יַמְתִּינוּ, אֶלָּא יֹאמְרוּ יִשְׁתַּבַּח וְיַמְתִּינוּ. וּכְשֶׁיָּבוֹאוּ עֲשָׂרָה, יֹאמְרוּ תְחִלָּה אֵיזֶה פְּסוּקִים וְאַחֲרֵיהֶם יֹאמַר הַשְּׁלִיחַ צִבּוּר חֲצִי קַדִּישׁ (נ"ג נ"ה ס"ט רל"ד).
After [completing] Yishtabach the chazzan says half-Kaddish.1Kaddish was instituted by the Anshei Knesses Hagedolah (the men of the Great Assembly) as a prayer of praise to offset the profaning of His Name resulting from the destruction of the First Temple and the Land of Israel. We pray that His Name be exalted and sanctified instead. Due to its great and awesome ramifications, our Sages wanted everyone to understand the meaning of this prayer and thus instituted that it be said in the spoken tongue; namely, Aramaic. There are also Kabbalistic reasons for the Kaddish being said in Aramaic. Kaddish, Barechu and Kedushah cannot be said and the Torah cannot be read unless there are ten adult men present. If ten men were not present when Yishtabach was said but, the minyan was completed afterwards, then, the chazzan may not say Kaddish, because Kaddish is said only following something that was said by ten men. They should, therefore, wait to say Yishtabach until ten [men] arrive. They may wait until almost a half-hour. They should not wait longer, but, rather, they should say Yishtabach and then wait. When ten [men] arrive they should first say a few verses, and afterwards the chazzan says half-Kaddish.
תנא דבי אליהו כל השונה הלכות בכל יום מובטח לו שהוא בן העולם הבא שנאמר הליכות עולם לו אל תקרי הליכות אלא הלכות (נדה ע"ג.)