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math.LO2025
A Gentle Introduction to the Axiom of Choice
Andreas Blass, Dhruv Kulshreshtha
This article offers a gentle introduction to the axiom of choice. We introduce the axiom, discuss some common objections to it, and present three kinds of reasons to accept it. Alt…
math.LO2024
A Reverse Mathematical Analysis of Hilbert's Nullstellensatz and Basis Theorem
Dhruv Kulshreshtha
This paper presents an expository reverse-mathematical analysis of two fundamental theorems in commutative algebra: Hilbert's Nullstellensatz and Basis Theorem. In addition to its…
math.LO2023
Cardinal Well-foundedness and Choice
Andreas Blass, Dhruv Kulshreshtha
We consider several notions of well-foundedness of cardinals in the absence of the Axiom of Choice. Some of these have been conflated by some authors, but we separate them carefull…