3 papers
math.LO2026
Effective Reducibility for Statements of Arbitrary Quantifier Complexity with Ordinal Turing Machines
Merlin Carl
This paper is an extended version of our work in \cite{Ca2025}. We extend the concept of effective reducibility between statements of set theory with ordinal Turing machines (OTMs)…
math.LO2026
Reduction Complexities in Set Theory
Merlin Carl
In \cite{Ca2016} and \cite{Ca2018}, we introduced a notion of effective reducibility between set-theoretical -statements; in \cite{Ca2025}, this was extended to statements…
math.LO2025
A Note on Power-OTMs
Merlin Carl
We consider the computational strength of Power-OTMs, i.e., ordinal Turing machines equipped with a power set operator, and study a notion of realizability based on these machines.…