Axiomatic Justification in Constructive Morse Set Theory

Mathematics > Logic [Submitted on 18 Jun 2026] Title:Axiomatic Justification in Constructive Morse Set Theory View PDF HTML (experimental)Abstract:Working within Constructive Morse Set Theory (CMST), we introduce axioms for a new notion, jst Pp, intended to capture what it means for P to prove, or justify, p under the BHK interpretation of intuitionistic logic. Since it makes no distinction between terms and formulae -- every term is also a formula, and vice versa -- CMST is well suited to our axiomatic development of justification theory within set theory itself. After stating our axioms for jst Pp, we derive many consequences thereof. In particular, we show that (with certain restrictions) our axioms for jst Pp align with the intended BHK interpretations of the axioms of intuitionistic logic. References & Citations Loading... Bibliographic and Citation Tools Bibliographic Explorer (What is the Explorer?) Connected Papers (What is Connected Papers?) Litmaps (What is Litmaps?) scite Smart Citations (What are Smart Citations?) Code, Data and Media Associated with this Article alphaXiv (What is alphaXiv?) CatalyzeX Code Finder for Papers (What is CatalyzeX?) DagsHub (What is DagsHub?) Gotit.pub (What is GotitPub?) Hugging Face (What is Huggingface?) ScienceCast (What is ScienceCast?) Demos Recommenders and Search Tools Influence Flower (What are Influence Flowers?) CORE Recommender (What is CORE?) arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.