Formalizing Ordinal Partition Relations Using Isabelle/HOL

  title={Formalizing Ordinal Partition Relations Using Isabelle/HOL},
  author={Mirna D{\vz}amonja and Angeliki Koutsoukou-Argyraki and Lawrence Charles Paulson},
  journal={Experimental Mathematics},
  pages={383 - 400}
ABSTRACT This is an overview of a formalization project in the proof assistant Isabelle/HOL of a number of research results in infinitary combinatorics and set theory (more specifically in ordinal partition relations) by Erdős–Milner, Specker, Larson and Nash-Williams, leading to Larson’s proof of the unpublished result by E.C. Milner asserting that for all , . This material has been recently formalised by Paulson and is available on the Archive of Formal Proofs; here we discuss some of the… 
Formalising Szemerédi's Regularity Lemma and Roth's Theorem on Arithmetic Progressions in Isabelle/HOL
. We have formalised Szemerédi’s Regularity Lemma and Roth’s Theorem on Arithmetic Progressions, two major results in extremal graph theory and additive combinatorics, using the proof assistant
Mathematical Proof Between Generations
. A proof is one of the most important concepts of mathematics. However, there is a striking difference between how a proof is defined in theory and how it is used in practice. This puts the unique
Wetzel: Formalisation of an Undecidable Problem Linked to the Continuum Hypothesis
. In 1964, Paul Erdős published a paper [5] settling a question about function spaces that he had seen in a problem book. Erdős proved that the answer was yes if and only if the continuum hypothesis
Towards Formalising Schutz' Axioms for Minkowski Spacetime in Isabelle/HOL
A mechanisation in Isabelle/HOL of the system of axioms as well as theorems relating to temporal order is presented, particularly where the formal work required additional steps, alternative approaches, or corrections to Schutz’ prose.


Zermelo Fraenkel Set Theory in Higher-Order Logic
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.
From LCF to Isabelle/HOL
This work focuses on Isabelle/HOL and its distinctive strengths, which include automatic proof search, borrowing techniques from the world of first order theorem proving, but also the automatic search for counterexamples.
Nitpick: A Counterexample Generator for Higher-Order Logic Based on a Relational Model Finder
Nitpick is a counterexample generator for Isabelle/HOL that builds on Kodkod, a SAT-based first-order relational model finder. Nitpick supports unbounded quantification, (co)inductive predicates and
On Fraisse's order type conjecture
ing from the embeddability relation between order types, define a quasi-order to be a reflexive, transitive relation. Throughout this paper, the letters Q and R will range over quasi-ordered sets and
The use of machines to assist in rigorous proof
  • R. Milner
  • Computer Science
    Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences
  • 1984
A method of tactic composition is presented in the form of an elementary theory of goal-seeking, by which simple elementary tactics are combined into more complex tactics, which may even be strategies complete for a class of problems.
A Machine-Checked Proof of the Odd Order Theorem
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.
Many of the problems Hajnal and I posed 15 years ago have been solved positively or negatively or shown to be undecidable. I state soae of the remaining ones and add a few new ones. I do not give a
Isabelle/HOL: A Proof Assistant for Higher-Order Logic
This presentation discusses Functional Programming in HOL, which aims to provide students with an understanding of the programming language through the lens of Haskell.
Borel sets and Ramsey's theorem
The main result is that all Borei sets are Ramsey, which was discovered independently by Andrzej Ehrenfeucht, Paul Cohen, and probably many others, but no proof has been published.
On the logical strength of Nash-Williams' theorem on transfinite sequences
We show that Nash-Williams' theorem asserting that the countable transfinite sequences of elements of a better-quasi-ordering ordered by embeddability form a better-quasi-ordering is provable in the