Overview
Current research
Natural induction (a model-theoretic study)
The above heading is the working title of my PhD thesis.
Chapter drafts
- Finitely non-standard models of Robinson arithmetic
- version: 2025-06-10
- Python and Coq sources referenced (and included verbatim) in the chapter:
- blog post announcement
Old material
What has now turned into my thesis project was previously “just” a research project, which went under the title ‘Necessarily non-analytic induction proofs’. The following is the material that I have previously made available—here on my website—under that title.
Most of this is very outdated. Some manuscripts contain errors that I have corrected in manuscripts not yet made public. Still all of the below material, corrected, reformulated or strengthened (‘or’ here being inclusive), will eventually find its way into my thesis. (In the meantime, anyone interested may contact me for unfinished manuscripts.)
For technical results see the summary. For a more conceptual discussion see the Stockholm Logic Seminar presentation. For slides, the JAF 38 presentation is more or less a condensed version of the FLoV Logic Seminar presentation (also, the linked blog post addresses some problems in the slides).
- Summary of results
- version 2020-01-22:
- all versions
- A note reflecting on terminology
-
JAF 38 presentation (2019)
- extended abstract (pdf)
- slides (pdf)
- blog post adressing some feedback
- The FLoV Logic Seminar
presentation (2019)
- slides (pdf)
- blog post adressing some feedback
- Stockholm Logic Seminar presentation (2017)
- MathOverflow: When must one strengthen one’s induction hypothesis? (2017)
- old material
- all files
Ellipsis usage in mathematics
- Stockholm PhD student seminar in theoretical philosophy
presentation (2018)
manuscript: - more material forthcoming
Past research
A Coq formalization of partial combinatory algebras and realizability
- GitHub repository:
https://github.com/anderslundstedt/pca-realizability - Realizability in Coq (2015)
- MSc thesis in Mathematics
- official repository
- A way to handle substitutions in first-order logic (2016)
- A note describing and motivating the formulation of first-order logic used
My BA thesis in philosophy
- Euklides princip och oändliga mängders storlek (2015)
[English: Euclid’s principle and the sizes of infinite sets]
My BSc thesis in Engineering Physics
- The Effects of Asset Return Correlation Errors in the Creditmetrics Framework (2011)
- official repository