Madhav Dhiman

collaborators

2 papers

math.GM2026

Non-Definability of Reachability in BÃ¼chi Arithmetic for a Family of Generalized Collatz Maps

Madhav Dhiman, Rohan Pandey

Let $q \geq 3$ and $d \geq 1$ be odd integers with $q + d$ a power of $2$ . We study the generalized Collatz map $T_{q, d}$ , a one-dimensional piecewise-affine map on the positive intege…

math.NT2026

Logical Undefinability of the Generalized Collatz Transition Relation in BÃ¼chi Arithmetic

Madhav Dhiman, Rohan Pandey

Let $q$ be an odd prime and let $d$ be an odd integer. We show that the arbitrary-step transition relation of the generalized Collatz map $T_{q, d}$ is not first-order definable in…