Recent Preprints
On The Categorical Structure of Decidability: A Topos-Theoretic Proof That Undecidable Statements Constitute The Norm
Prabahan Dey
January 2, 2026
Abstract: We establish a categorical characterization of decidability within formal systems interpreted in topoi. For any topos T with subobject classifier Ω and any formal system object F satisfying standard computability conditions, we prove that the characteristic morphism classifying decidable statements necessarily factors through a proper subobject of Ω corresponding to recursively enumerable truth values. This factorization provides a structural account of why decidable statements form a restricted class within the broader landscape of well-formed statements.
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Topos Preprints accepts original research in categorical logic, topos theory, type theory, and related areas of mathematics.
Submission Guidelines
We accept papers in the following areas:
- Topos theory and categorical logic
- Higher category theory and higher topos theory
- Type theory and homotopy type theory
- Categorical semantics and proof theory
- Sheaf theory and categorical algebraic geometry
- Effective topos theory and realizability
- Applications of categorical methods to logic and foundations
Requirements
- Papers must present original research
- Mathematical content must be rigorous
- PDF format preferred
- Include title, author(s), date, and abstract
- Papers are reviewed for quality and relevance (typically within 48-72 hours)
How to Submit
Send your preprint to: deyprabahan@gmail.com
Please include in your email:
- Paper PDF as attachment
- Title of the paper
- Author name(s) and affiliation(s) (if any)
- Brief abstract (can be copied from paper)
- Any relevant keywords or subject classifications
Note: Topos Preprints is an open archive. By submitting, you agree to make your work publicly available. This does not prevent subsequent journal publication.
About Topos Preprints
Mission
Topos Preprints is an open preprint repository dedicated to categorical logic, topos theory, and related fields. We provide a platform for researchers to share their work freely, without institutional barriers.
Philosophy
Mathematics thrives on open exchange of ideas. Traditional preprint servers often impose institutional requirements that exclude independent researchers and mathematicians from underrepresented regions. Topos Preprints aims to democratize access to mathematical publication while maintaining rigorous standards.
Scope
We accept papers in:
- Topos theory and categorical logic
- Higher category theory
- Type theory and proof assistants
- Categorical semantics
- Sheaf theory and descent
- Effective mathematics and realizability
- Categorical foundations of mathematics
Quality Control
All submissions are reviewed for mathematical rigor and relevance. We filter out:
- Papers with fundamental mathematical errors
- Work that does not engage with the categorical literature
- Submissions that misuse technical terminology
- Non-mathematical content
However, we welcome exploratory work, negative results, and papers that challenge conventional perspectives, provided they maintain mathematical standards.
Contact
For questions, suggestions, or submission inquiries: deyprabahan@gmail.com