Nihal Uppugunduri's WebsiteIn this exploration, we generalize the theory of bases in vector spaces to other settings involving “generation” by subsets, inspired by our work with “logical bases” of classes of models (see my previous exploration for context on that.) We can even try to see how this relates to concepts like the free object.
In this post, we consider the following:
Conjecture. Let 
We discuss some lemmas for functions on sets, which I wrote up some time ago to clarify and better understand the nature of 
We continue the discussion from this post.
In this post, we continue the discussion from the previous in the series.
Can we formalize the notion of two axiomatic systems being “equivalent,” especially when they are over different languages?
We continue the discussion started in this post.
In this post, we consider a variation of a unique factorization domain (UFD) that can more closely align with our intuition for prime factorization of integers — specifically, rather than the factorization being required to be up to invertible elements, here we require the factorization to be up to multiplicative identity. This is a seemingly stronger definition, and one that doesn’t seem to encompass fields trivially or obviously (in line with our intuition for integer prime factorization.)
We continue the discussion from the previous post in the series.
In this post, we try to tease out more motivation and a better systematization of analytic number theory, which traditionally has been viewed more as a collection of ad-hoc concepts. This may end up including new concepts that aren’t yet part of the standard literature, and hopefully these can yield more fruit in the subject.
