Question: Under what union did the king who created Duchy of Holstein serve?

full_context: Document 1: Schleswig-Holstein-Sonderburg: Schleswig-Holstein-Sonderburg was the name of a branch line of the House of Oldenburg as well as the name of their land. It existed from 1564 until 1668 and was a titular duchy under the King of Denmark, rather than a true territorial dukedom in its own right. The seat of the duke was Sonderburg. Parts of the domain were located in Denmark (in the Duchy of Schleswig), mainly on the islands of Als and Ærø and around Glücksburg, whilst other lands were part of the Holy Roman Empire (in the Duchy of Holstein), including the "Ämter" of Plön, Ahrensbök, and Reinfeld. As a result of various inheritance arrangements it fragmented into numerous small territories which were eventually absorbed into Greater Denmark in the 18th century.
Document 2: Duchy of Holstein: The Duchy of Holstein (German: "Herzogtum Holstein" , Danish: "Hertugdømmet Holsten" ) was the northernmost state of the Holy Roman Empire, located in the present German state of Schleswig-Holstein. It was established when King Christian I of Denmark had his County of Holstein-Rendsburg elevated to a duchy by Emperor Frederick III in 1474. Holstein was ruled jointly with the Duchy of Schleswig by members of the Danish House of Oldenburg for its entire existence.
Document 3: Flag of Prussia: The state of Prussia had its origins in the separate lands of the Margraviate of Brandenburg and of the Duchy of Prussia. The Margraviate of Brandenburg developed from the medieval Northern March of the Holy Roman Empire, passing to the House of Hohenzollern in 1415. The Duchy of Prussia originated in 1525 when Albert of Brandenburg-Ansbach, a member of a cadet branch of the Hohenzollerns, secularized the eastern lands of the Teutonic Knights as a Polish fief. Prince-elector John Sigismund, Elector of Brandenburg, inherited the Duchy of Prussia in 1618, thus uniting Brandenburg and Prussia under one ruler in a personal union; the Elector's state became known as Brandenburg-Prussia. The Kingdom of Prussia formed when Elector Frederick III assumed the title of Frederick I, King in Prussia, on 18 January 1701.
Document 4: Province of Schleswig-Holstein: The Province of Schleswig-Holstein (German: "Provinz Schleswig-Holstein" , ] ) was a province of the Kingdom of Prussia and the Free State of Prussia from 1868 to 1946. It was created from the Duchies of Schleswig and Holstein, which had been conquered by Prussia and the Austrian Empire from Denmark in the Second War of Schleswig in 1864. Following the Austro-Prussian War in 1866, which ended in Austrian defeat, Schleswig and Holstein were annexed by Prussia. The province was created in 1868 and also included the Duchy of Lauenburg since 1876.
Document 5: Schleswig-Holstein-Sonderburg-Plön: The Duchy of Schleswig-Holstein-Sonderburg-Plön (German: "Herzogtum Schleswig-Holstein-Sonderburg-Plön" ), also "Schleswig-Holstein-Plön", "Holstein-Plön" or just "Duchy of Plön", was a small sub-duchy ("Teilherzogtum") created by the physical division of the Duchy of Schleswig-Holstein-Sonderburg. Today, its remaining significance is primarily the building of Plön Castle. The Duchy of Plön was not a territorial dukedom in its own right, but a sub-division within the state structure of the duchies of Schleswig and Holstein. The scattered territorial dominion lay mostly in the southeast part of present-day German state of Schleswig-Holstein.
Document 6: List of consorts of Schleswig and Holstein: The Duchesses of Schleswig-Holstein were the consorts of the rulers of Schleswig-Holstein and the separate states of Schleswig and Holstein, before that, the two duchies of Schleswig and Holstein. This article would focus more on the Duchess consorts of Schleswig and Holstein, Schleswig-Holstein (in pretense), and the many branches of the Schleswig-Holstein duchy created by the Danish king for his relatives.
Document 7: Denmark–Norway: Denmark–Norway (Danish and Norwegian: "Danmark–Norge ") was an early modern multi-national and multi-lingual real union consisting of the Kingdom of Denmark, the Kingdom of Norway (including Norwegian regions Faroe Islands, Iceland, Greenland, et cetera), the Duchy of Schleswig, and the Duchy of Holstein. The state also claimed sovereignty over two historical peoples: Wends and Goths. In addition, the state included colonies: St. Thomas, St. John, St. Croix, Ghana, Tharangambadi, Serampore, and Nicobar Islands. The state's inhabitants were mainly Danes, Norwegians (along with Inuit and Sami), and Germans. The state's largest cities were Copenhagen, Altona, Bergen, Trondheim, and Christiania (Oslo).
Document 8: John, King of Denmark: John (Danish and Norwegian: "Hans" ; Swedish: "Johan" ; né "Johannes") (2 February 1455 – 20 February 1513) was a Scandinavian monarch under the Kalmar Union. He was King of Denmark (1481–1513), Norway (1483–1513) and as John II (Swedish: "Johan II" ) Sweden (1497–1501). From 1482 to 1513, he was concurrently Duke of Schleswig and Holstein in joint rule with his brother Frederick. He currently remains the only King of Denmark since the mid-15th century to not be named Christian or Frederick, if one does not include the current Queen of Denmark, Margrethe II.
Document 9: Frederick I of Denmark: Frederick I (7 October 1471 – 10 April 1533) was the King of Denmark and Norway. His name is also spelled "Friedrich" in German, "Frederik" in Danish and Norwegian and "Fredrik" in Swedish. He was the penultimate Roman Catholic monarch to reign over Denmark, when subsequent monarchs embraced Lutheranism after the Protestant Reformation. As King of Norway, Frederick is most remarkable in never having visited the country and was never being crowned King of Norway. Therefore he was styled "King of Denmark, the Vends and the Goths, elected King of Norway".
Document 10: Treaty of Ribe: The Treaty of Ribe (Danish: "Ribe-brevet" meaning The Ribe letter; German: "Vertrag von Ripen" ) was a proclamation at Ribe made by King Christian I of Denmark to a number of Holsatian nobles enabling himself to become Count of Holstein and regain control of Denmark's lost Duchy of Schleswig (Danish: "Sønderjylland", i.e. "South Jutland"). The most famous line of the proclamation was that the Danish Duchy of Schleswig and the County of Holstein within the Holy Roman Empire, should now be, in the original Middle Low German language, "Up Ewig Ungedeelt", or "Forever Undivided". This was to assume great importance as the slogan of German nationalists in the struggles of the 19th century, under completely different circumstances.
Document 11: Frederick I of Denmark: Frederick I (7 October 1471 – 10 April 1533) was the King of Denmark and Norway. His name is also spelled "Friedrich" in German, "Frederik" in Danish and Norwegian and "Fredrik" in Swedish. He was the penultimate Roman Catholic monarch to reign over Denmark, when subsequent monarchs embraced Lutheranism after the Protestant Reformation. As King of Norway, Frederick is most remarkable in never having visited the country and was never being crowned King of Norway. Therefore he was styled "King of Denmark, the Vends and the Goths, elected King of Norway".
Document 12: Christian I of Denmark: Christian I (February 1426 – 21 May 1481) was a Scandinavian monarch under the Kalmar Union. He was King of Denmark (1448–1481), Norway (1450–1481) and Sweden (1457–1464). From 1460 to 1481, he was also Duke of Schleswig (within Denmark) and Count (after 1474, Duke) of Holstein (within the Holy Roman Empire). He was the first Danish monarch of the House of Oldenburg.
Document 13: Christopher I of Denmark: Christopher I (Danish: "Christoffer I" ) (1219 – 29 May 1259) was King of Denmark between 1252 and 1259. He was the son of Valdemar II of Denmark by his wife, Infanta Berengária of Portugal. He succeeded his brothers Eric IV Plovpenning and Abel of Denmark on the throne. Christopher was elected King upon the death of his older brother Abel in the summer of 1252. He was crowned at Lund Cathedral on Christmas Day 1252.
Document 14: Christian VIII of Denmark: Christian VIII (18 September 1786 – 20 January 1848) was the King of Denmark from 1839 to 1848 and, as Christian Frederick, King of Norway in 1814.
Document 15: Christopher of Bavaria: Christopher of Bavaria (26 February 1416 – 5/6 January 1448) was King of Denmark (1440–48, as Christopher III), Sweden (1441–48) and Norway (1442–48) during the era of the Kalmar Union.
ground_truth: the Kalmar Union