Related papers: The Definability Strength of Combinatorial Princip…
We consider Proof Complexity in light of the unusual binary encoding of certain combinatorial principles. We contrast this Proof Complexity with the normal unary encoding in several refutation systems, based on Resolution and Integer Linear…
In Pure Inductive Logic, the principle of Strong Predicate Exchangeability is a rational principle based on symmetry that sits in between the principles of Predicate Exchangeability and Atom Exchangeability. We will show a de Finetti -…
One way of studying a relational structure is to investigate functions which are related to that structure and which leave certain aspects of the structure invariant. Examples are the automorphism group, the self-embedding monoid, the…
This article is an introduction to combinatorics under the axiom of determinacy with a focus on partition properties and infinity Borel codes.
In order to make argumentation-based inference contestable, it is crucial to explain what changes can achieve a desired (instead of the contested) inference result. To this end, we introduce strength change explanations for quantitative…
Continuous reducibilities are a proven tool in computable analysis, and have applications in other fields such as constructive mathematics or reverse mathematics. We study the order-theoretic properties of several variants of the two most…
Combinatorics, like computer science, often has to deal with large objects of unspecified (or unusable) structure. One powerful way to deal with such an arbitrary object is to decompose it into more usable components. In particular, it has…
We study the theoretical structure of compositeness with explicit energy dependence, and find a possible explanation for the difficulty in the interpretation of compositeness of deuteron. Compositeness of deuteron is calculated as larger…
Promoting a theory with a finite number of terms into an effective field theory with an infinite number of terms worsens simplicity, predictability, falsifiability, and other attributes often favored in theory choice. However, the…
The forcing theorem is the most fundamental result about set forcing, stating that the forcing relation for any set forcing is definable and that the truth lemma holds, that is everything that holds in a generic extension is forced by a…
In this article, we prove that Ramsey's theorem for pairs and two colors is $\Pi^1_1$-conservative over~$\mathsf{RCA}_0 + \mathsf{B}\Sigma^0_2 + \mathsf{WF}(\epsilon_0)$ and over~$\mathsf{RCA}_0 + \mathsf{B}\Sigma^0_2 + \bigcup_n…
The paper is devoted to the study of combinatorial determinacy properties of a family of substitution complexes consisting of quadrilaterals glued side-to-side with each other. These properties are useful in constructing algebraic…
We prove upper and lower bounds on the effective content and logical strength for a variety of natural restrictions of Hindman's Finite Sums Theorem. For example, we show that Hindman's Theorem for sums of length at most 2 and 4 colors…
We answer a question posed by Hirschfeldt and Jockusch by showing that whenever $k > \ell$, Ramsey's theorem for singletons and $k$-colorings, $\mathsf{RT}^1_k$, is not strongly computably reducible to the stable Ramsey's theorem for…
We look at characterizing which formulas are expressible in rich decidable logics such as guarded fixpoint logic, unary negation fixpoint logic, and guarded negation fixpoint logic. We consider semantic characterizations of definability, as…
Recent advances in our understanding of higher derived limits carry multiple implications in the fields of condensed and pyknotic mathematics, as well as for the study of strong homology. These implications are thematically diverse,…
We complete a 40-year old program on the computability-theoretic analysis of Ramsey's theorem, starting with Jockusch in 1972, and improving a result of Chong, Slaman and Yang in 2014. Given a set $X$, let $[X]^n$ be the collection of all…
We study combinatorial configurations with the associated point and line graphs being strongly regular. Examples not belonging to known classes such as partial geometries and their generalizations or elliptic semiplanes are constructed.…
We show that for every finite colouring of the natural numbers there exists $a,b >1$ such that the triple $\{a,b,a^b\}$ is monochromatic. We go on to show the partition regularity of a much richer class of patterns involving exponentiation.…
We deal with the combinatorial principle Weak Diamond, showing that we always either a local version is not saturated or we can increase the number of colours. Then we point out a model theoretic consequence of Weak Diamond.