Presentation of the Kanamori-McAloon Theorem

The Kanamori-McAloon theorem demonstrates that there are combinatorial statements which Peano Arithmetic cannot prove. The theorem can be viewed as an instance of Gödel’s incompleteness theorem, as it demonstrates specific statements wich are independent of Peano-Arithmetik. Additionally, this shows that Zermelo-Fraenkel set theory (ZFC) is actually stronger than Peano Arithmetic, as ZFC can prove the truth of these combinatorial statements.

This script is based on Chapter 14 of "Models of Peano Arithmetic" by Richard Kaye (1991). I wrote it for a presentation in the seminar on "Models of Peano Arithmetic," led by Ralf Schindler and Martin Hils at the University of Münster. If you find any mistakes or have any questions, feel free to contact me!

Thesis on the Theorem of Linström

Lindström’s theorem states that first-order predicate logic is the most expressive logic satisfying the compactness theorem and the Löwenheim-Skolem theorem. This result not only justifies the prominent status of first-order predicate logic in mathematical logic but also attributes axiomatic status to the Löwenheim-Skolem theorem and the compactness theorem within this framework.

This bachelor's thesis is primarily based on Ebbinghaus’ introduction to mathematical logic, chapter 13 (“Einführung in die mathematische Logik”, Berlin, 2018).

Hausarbeit zur Modellbeziehung in der math. Logik

Die Arbeit behandelt die Modellbeziehung in der Modelltheorie, die beschreibt, welche Formeln in einer Struktur gelten. Sie ist in zwei Teile geteilt: Der erste Teil führt in die Grundlagen ein und konzentriert sich auf die Ausdruckskraft von Formeln. Der zweite Teil klassifiziert Formelmengen nach der Präzision, mit der sie Modelle beschreiben. Der Schwerpunkt liegt auf der Modellbeziehung und dem Verhältnis von Objekt- zu Metasprache, mit einem Überblick über philosophisch relevante Eigenschaften.

Zur Bedingung der Möglichkeit von Erfahrung. Eine modallogische Analyse (peer reviewed)

In Kantian philosophy, the term “condition of possibility” is central, but carries the following ambiguity. According to one reading, “condition of possibility” merely means “necessary condition”. However, it is demonstrated that a deeper interpretation of the term “possibility” proves to be more fruitful. This reading allows us to reconstruct an important background assumption of Kant: Every condition of the possibility of experience holds necessarily, provided that experience is possible. Or more generally: All conditions of the possibility hold necessarily as long as the conditioned is actually possible.

This conclusion is understood through the axiomatic system S5. Therefore I argue by referencing the schematism chapter that Kant’s notion of modal terms can be formalized through S5.