You're describing a form of social housing.

No. Because HDBs are not owned by the government.

Yes. Because "social housing" is a general term that implies subsidization and affordability rather than any one specific ownership model.

No. Social housing is government owned and rented. Singapore is government built and sold. Singapore is a tiny island with little space. The government has to control what is built where and avoids it turning into Hong Kong slums.

You're being stubborn. From Wikipedia:

>Public housing, also known as social housing, is subsidized or affordable housing provided in buildings that are usually owned and managed by local government, central government, nonprofit organizations or a combination thereof.