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math.LO2026
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.LO2024
The Logic of Cardinality Comparison Without the Axiom of Choice
Matthew Harrison-Trainor, Dhruv Kulshreshtha
We work in the setting of Zermelo-Fraenkel set theory without assuming the Axiom of Choice. We consider sets with the Boolean operations together with the additional structure of c…