In a sentence like Taivas on sininen (The sky is blue), the last word is called the predicative instead of the object, since the verb olla (to be) is not regarding as having an object. The case of the predicative is the nominative, as in the example above, or the partitive, as in the statement Vesi on kylmää (The water is cold).
The predicative is in plural, if the subject is in plural form, e.g. Nämä autot ovat uusia (These cars are new).
In addition to normal predicatives, there is also the genitive predicative, as in Talo on minun (The house is mine). It can be understood as a short form of an expression like Talo on minun taloni (The house is my house), where the genitive is an attribute. For this reason, it is natural that the genitive predicative is in plural according to the number of the “possessor”, not of the possessed. For example, we say Talot ovat minun (The houses are mine), Talo on meidän (The house is ours).
If a personal pronoun appears as a genitive predicative, the normal genitive form is used. Finnish has no distinction such as “yours” versus “your” in English.
An adjective used as a predicative is in the nominative, e.g. Poika on surullinen (The boy is sad), unless there is a special reason to use the partitive, namely one of the following:
When a noun is used as a predicative, it is in the nominative if in singular, but usually in the partitive if in plural. For example, Hän on tyttäreni (She is my daughter) but He ovat tyttäriäni (They are my daughters). Similarly, we say Suomalaiset ovat ujoja (Finns are shy). Foreigners who have learned Finnish often mistakenly use the nominative (ujot) here, since there does not seem to be any logical reason for the partitive.
It is also possible to have the subject in singular and the predicative in partitive plural, e.g. Hän on Maijan tyttäriä (She is one of the daughters of Maija). This differs in tone from Hän on yksi Maijan tyttäristä, which emphasizes the “one of” part. These both differ from Hän on Maijan tytär (She is Maija’s daughter), which does not imply (or deny) the existence of other daughters.
The predicative can be in the nominative even in plural, but this changes the meaning: the predicative then refers to a definite, known set. For example, Nämä ovat Maijan tyttäret (These are the daughters of Maija) means that all daughters of Maija are being referred to, as opposite to Nämä ovat Maijan tyttäriä (These are daughters of Maija).
The partitive is also used if the predicative is a mass noun, referring to a substance, such as in Nämä kengät ovat nahkaa (These shoes are made of leather). The same applies if the subject is a mass noun, e.g. Vesi on kylmää (The water is cold). Abstract properties and names of actions are also treated as mass nouns, e.g. Vaikeneminen on kultaa (Silence is golden; literally “Being silent is gold”). The same applies to demonstrative pronouns when their meaning is abstract and not a physical entity, e.g. Tämä on hauskaa (This is fun), but Tämä on älypuhelin (This is a smartphone).
Some nouns can be treated as mass nouns or otherwise. We can say Hänen elämänsä on vaikeaa (His life is hard) in the partitive, but Hänen elämänsä oli lyhyt (His life was short), since here elämä does not refer to life in general but to the duration of a person’s life, lifetime. Similarly, we normally say Tässä on vettä (Here is [some] water), but when referring to some specific amount of water that has been mentioned, we say Tässä on vesi (Here is the water).