I What is the official name for a Field Series in mathematics/physics?

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The term "field series" in mathematics and physics refers to a sequence of fields, often defined in the context of a tower of fields where each field is contained within the next. The concept requires user-defined parameters to clarify what is meant by "field" and "series." The discussion highlights the need for precise terminology when developing concepts like infinitesimal recursion or continuous hierarchy. There is no widely recognized official name for "field series," indicating a gap in existing literature. Clear definitions are essential for effective communication in this area of study.
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What is the official name for a field series in mathematics/physics?
I've been working on developing infinitesimal recursion (what I call continuous hierarchy), but I ended up arriving at "field series" instead. My searches didn't seem to come up with anything reasonable (battlefield the video game series), so I'm wondering what the official name for a field series is. Thanks!
 
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What do you mean by field and what by series? Fields are certain rings, and related ones are sometimes a tower of fields or a sequence of fields in case they are contained in one another.
 
Needs to be user defined.
 

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