(a)      A child born to parents who have not participated in a marriage ceremony with each other shall be considered to be the child of his mother.

      (b)      A child born to parents who have not participated in a marriage ceremony with each other shall be considered to be the child of his father only if the father:

            (1)      Has been judicially determined to be the father in an action brought under the statutes relating to paternity proceedings;

            (2)      Has acknowledged himself, in writing, to be the father;

            (3)      Has openly and notoriously recognized the child to be his child; or

            (4)      Has subsequently married the mother and has acknowledged himself, orally or in writing, to be the father.