QTower Algebra introduces a unifying algebra for iterative meta‑reasoning. We formalize a Qtower as the the sequence Q, □Q, □□Q, … and analyze it in a Boolean‑algebra‑of‑operators setting where the modal operator □ acts levelwise. This paper covers QTowers which refers to n-Tuples (Q1,. . . Qi,. . Qn) consisting of Q1 = A base Question and Qi="Is Qi-1 provable? " For all i >=2. , Answer Mapings A: Q->True, False and exhibits connections to many different areas of Mathematics and Theoretical Computer Science. Topics include: Representing irational numbers with QTowers Perfectoid Logical Rings Hilberts Hotel, Busy Beaver Graphs and QTowers Linear Time Logik Proof Stability and new in V1. 2 The Gödel Gap Mini QTowers and LLMs/Transformer Architecture "The Trickster" Anouncement: A short introductionary version of QTower Algebra is being worked on. I like to thank the academic community for their strong interest in QTower Algebra. This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4. 0 International License (CC BY-NC-SA 4. 0).
Christian Oppel (Mon,) studied this question.