Literature

My Publications

Here is a list of my publications related to this topic. You find some of them on .

1. Infinity is Not a Size. The Logica Yearbook 2020, 33-48, 2021, .
2. A Model Theory for the Potential Infinite. Reports on Mathematical Logic 57, 3-30, 2022, and .
3. Higher-Order Concepts for the Potential Infinite. Theoretical Computer Science, 2023, .
4. A Reflection Principle for Potential Infinite Models of Type Theory. Post-proceedings of the conference TYPES 2023, LIPIcs, Volume 303, 2024, and .
5. Continuity in Potential Infinite Models, 2025, .

My Talks

There are some slides from talks that I gave in the past.

1. It’s a Matter of Dependency, Not of Size. Slides from talk in a senior seminar at LMU Munich, October 2017, .
2. Finitistic Higher Order Logic. Slides from a working meeting between LMU Munich and University of Bern, December 2017, .
3. Indefinitely Extensible Models and a Relative Infinite. Slides from the 12th Panhellenic Logic Symposium in Anogeia, June 2019, .
4. A Relative Infinite. Slides from a working meeting between LMU Munich, University of Bern and University of Verona, December 2019, .
5. Continuity for Computability. Slides from the CCC 2021 (Continuity, Computability, Constructivity) conference, September 2021, .
6. Taking Indefinite Extensibility Seriously. Slides from the UNILOG 2022 conference in Crete, April 2022, .
7. Don’t Forget the Universal Quantifier. Slides from the conference Proof and Computation in Kloster Schlehdorf, June 2022, .
8. Dynamic Type Theory. Extended abstract and slides from the conference TYPES in Valencia, June 2023, (extended abstract) and (slides).
9. Formalizing the Potential Infinite. Slides from talk in a senior seminar at LMU Munich, February 2024, .
10. Indefinitely Extensible Models of Simple Type Theory. Slides from a talk at the Logic Colloquium 2024 in Gothenburg, June 2024, (slides) and (poster).

Other Literature

These are pointers to some books, papers, presentations and projects. This list is neither complete nor representative, but related to my project.

1. Fletcher, Peter. Truth, Proof and Infinity: A Theory of Constructive Reasoning. Vol. 276. Springer Science & Business Media, 2013.
2. Fletcher, Peter. Infinity. Philosophy of Logic. North-Holland, 2007. 523-585. Pre-print
3. Lavine, Shaughan. Understanding the infinite. Harvard University Press, 1994.
4. Linnebo, Øystein, and Stewart Shapiro. Actual and potential infinity. Noûs 53.1 (2019): 160-191.
5. Mawby, Jim. Strict finitism as a foundation for mathematics. Diss. University of Glasgow, 2005.
6. Mycielski, Jan. Locally finite theories. The Journal of Symbolic Logic 51.1 (1986): 59-62.
7. Sereno, Lisa Ann. Infinity and experience. Diss. Massachusetts Institute of Technology, 1998.
8. Shapiro, Stewart, and Crispin Wright. All things indefinitely extensible. Absolute generality (2006): 255-304.
9. Styrman, Avril. Potential infinity and natural numbers. La Nuova Critica 57 (2011): 7-23.
10. Van Bendegem, Jean Paul. Why the largest number imaginable is still a finite number. Logique et Analyse 42.165/166 (1999): 107-126.
11. Van Bendegem, Jean Paul. A Defense of Strict Finitism. Constructivist Foundations 7.2 (2012).
12. The project Infinity in Mathematics at the University of Oslo.

About Me

Matthias Eberl

I studied mathematics and theoretical physics at the LMU (Ludwig-Maximilians-Universität) Munich and accomplished my PhD in 2002 under the supervision of Helmut Schwichtenberg. My research area is mathematical logic. I became interested in infinity around 2015 when I found no convincing mathematical formulation of the potential infinite.

Contact

You can contact me on any issue related to the topics mentioned on my website. Please send an email to matthiasREMOVEMEde.

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