Bava Batra 127: Who is Male in Order to Inherit? A Father's Word About his Son's Identity

Who counts as a firstborn when it comes to inheritance?  Must sons be recognizable as male from birth?  The rabbis speak about proofs that a son was male from birth: circumcision at eight days and his mother's status as tumah for 33 and not 66 days.  This leads to a conversation about the guidelines regarding tumah after the birth of a tumtum, an androgynos, or another child whose sex is in doubt.  

What is done when two children might be the firstborn?  The rabbis create procedures that allow the two to share their inheritance.  One signs a document allowing the other to have power of attorney, and the two divide the remaining portion between them.  

Is a father believed when he states that one son is his firstborn because the other was born to a divorcee or a chalutza?  The rabbis discuss why we might not believe the father's statement and why we might trust his statement.  

And what about a retraction?  If a father says that a boy is his son and then he says that the boy is his slave, is he believed?  The rabbis suggest that one who corrects himself in the other direction is telling the truth.  Further, if his statement is that his son serves him like a slave, it can be retracted.  It is understood that a father would not knowingly call his son his slave.  The status of a slave was clearly very defined and very far below that of a son.