## 40 References

### Formalizing Ordinal Partition Relations Using Isabelle/HOL

- 2022

Computer Science

Exp. Math.

An overview of a formalization project in the proof assistant Isabelle/HOL of a number of research results in infinitary combinatorics and set theory by Erdős–Milner, Specker, Larson and Nash-Williams, leading to Larson's proof of the unpublished result by E.C. Milner asserting that for all.

### A Machine-Checked Proof of the Odd Order Theorem

- 2013

Mathematics

ITP

This paper reports on a six-year collaborative effort that culminated in a complete formalization of a proof of the Feit-Thompson Odd Order Theorem in the Coq proof assistant, using a comprehensive set of reusable libraries of formalized mathematics.

### A Ramsey theorem in Boyer-Moore logic

- 2004

Mathematics

Journal of Automated Reasoning

The Boyer-Moore Prover, Nqthm, is used to verify the Paris-Harrington version of Ramsey's theorem, which is not provable in Peano Arithmetic, and one key step in the proof requires ε0 induction.

### A Partition Calculus in Set Theory

- 1956

Mathematics

Dedekind’s pigeon-hole principle, also known as the box argument or the chest of drawers argument (Schubfachprinzip) can be described, rather vaguely, as follows. If sufficiently many objects are…

### Formalizing an Analytic Proof of the Prime Number Theorem

- 2009

Mathematics

Journal of Automated Reasoning

This work describes the computer formalization of a complex-analytic proof of the Prime Number Theorem (PNT), a classic result from number theory characterizing the asymptotic density of the primes, and analyzes the relationship between the formal proof and its informal counterpart.

### A Theorem in the Partition Calculus

- 1972

Mathematics

Canadian Mathematical Bulletin

If S is an ordered set we write tp S to denote the order type of S and |5| for the cardinal of S. We also write [S] k for the set {X:X ⊂ S, |X|=k}. The partition symbol (1)

### A Theorem in the Partition Calculus Corrigendum

- 1974

Mathematics

Canadian Mathematical Bulletin

In order to make (19) correct we define X., S(n) (n<(o) a little more caref lly and replace lines 21-31 on Page 504 by the following : Let n < co and s ppose that we have already chosen elements xi c…

### A partition theorem

- 1966

Mathematics

We prove a partition theorem (in the sense of the theorems of Ramsey [3], Erdos-Rado [1], and Rado [2]) which together with a forthcoming paper by Halpern and A. Levy will constitute a proof of the…

### Simple Type Theory is not too Simple: Grothendieck’s Schemes Without Dependent Types

- 2022

Mathematics

Exp. Math.

This experiment shows that the simple type theory implemented in Isabelle can handle such elaborate constructions despite doubts raised about Isabelle’s capability in that direction.

### Zermelo Fraenkel Set Theory in Higher-Order Logic

- 2019

Mathematics

Arch. Formal Proofs

The theory provides two type classes with the aim of facilitating developments that combine V with other Isabelle/HOL types: embeddable, the class of types that can be injected into V (including V itself as well as V*V, V list, etc.), and small, theclasses that correspond to some ZF set.