A Nested Hierarchy of Male Descendants?

On another discussion board a Franky172 has changed the idea of a paternal family tree to a scheme of all male descendants ox x, including x. Read the stupidity for yourselves here

But is that scheme a nested hierarchy?

A reminder of the rules of hierarchy:

Summary of the Principles of Hierarchy Theory:

With a paternal family tree the sets are determined by ONE AND ONLY ONE criterion- "who's your daddy?"

Hierarchical levels: levels are populated by entities whose properties characterize the level in question.

Note the word "properties".

Level of organization: this type of level fits into its hierarchy by virtue of set of definitions that lock the level in question to those above and below.

Note the words "set of definitions"

The ordering of levels: there are several criteria whereby other levels reside above lower levels.

Note the words "several criteria".

To re-iterarte- With a paternal family tree levels are determined by ONE and only ONE criterion- “Who’s your daddy?”

Nested and non-nested hierarchies: nested hierarchies involve levels which consist of, and contain, lower levels. Non-nested hierarchies are more general in that the requirement of containment of lower levels is relaxed. For example, an army consists of a collection of soldiers and is made up of them. Thus an army is a nested hierarchy. On the other hand, the general at the top of a military command does not consist of his soldiers and so the military command is a non-nested hierarchy with regard to the soldiers in the army. Pecking orders and a food chains are also non-nested hierarchies.

Now in a scheme of all male descendants of x, including x what would be the properties that characterize the level in question?

What are the set of definitions that lock a level in question to those above and below it?

What are the several criteria whereby other levels reside above lower levels?

And for the clincher- what is done to the male descendants that are born of female descendants? How are they tied to the top level?

Questions like these arise and usually go unanswered when people, who don't know what they are doing, try to establish something anyway.

It is obvious that Franky172 doesn't realize that his:

D{x, all male descendabts of x} translates to D(sam) only when Sam doesn't have any male descendants.

Once Sam has a male descendant the scheme looks like:

_______________D(sam, sam's first male descendant)
_______________|
_______________D(sam's first male descdendant)

When the next male descenfdant arrives the scheme changes to, oops we may have a problem without specifically defined levels:

______________D(sam, sam's first male descendant, sam's second male descendant)

The definition of levels is key here. Would the first level below the starting node od D{x, all male descendants of x} be reserved for Sam's sons?

What happens when Sam's first male descendant isn't Sam's son but the son of one of Sam's daughters?

Without well-defined levels any alleged "nested hierarchy" dissolves into jibberish.