逻辑
The notion of well order admits an alternative definition in terms of embeddings between initial segments. We use the framework of reverse mathematics to investigate the logical strength of this definition and its connection with…
We are studying the degrees in which a computable structure is relatively computably categoricity, i.e., computably categorcial among all non-computable copies of the structure. Unlike the degrees of computable categoricity we can bound the…
We formally investigate immediate and mediate grounding operators from an inferential perspective. We discuss the differences in behaviour displayed by several grounding operators and consider a general distinction between grounding and…
Motivated by two open questions about two-cardinal tree properties, we introduce and study generalized narrow system properties. The first of these questions asks whether the strong tree property at a regular cardinal $\kappa \geq \omega_2$…
We give a proof-theoretic as well as a semantic characterization of a logic in the signature with conjunction, disjunction, negation, and the universal and existential quantifiers that we suggest has a certain fundamental status. We present…
Modulo the existence of large cardinals, there is a model of set theory in which for some set $B$ of regular cardinals, the sequence $\langle \text{pcf}^\alpha(B): \alpha \in \text{Ord} \rangle$ is strictly increasing. The result answers a…
This book is a course in Stone-Priestley duality theory, with applications to logic and theoretical computer science. Our target audience are graduate students and researchers in mathematics and computer science. Our aim is to get in a…
This paper develops techniques which are used to answer a number of questions in the theory of equivalence relations generated by continuous actions of abelian groups. The methods center around the construction of certain specialized…
We show that the countable universal omega-categorical bowtie-free graph admits generic automorphisms. Moreover, we show that this graph is not finitely homogenisable.
The aim of this paper is to prove that for there exist a chain in the Rudin-Frol\'ik order of $\beta\kappa\setminus \kappa$ of length $\mu$ with $\kappa \leqslant \mu \leqslant 2^\kappa$ for regular $\kappa> \omega$ without a lower bound.
A variation of the Scott analysis of countable structures is applied to actions of non-Archimedean TSI Polish groups acting continuously on a Polish spaces. We give results on the potential Borel complexity spectrum of such groups, and…
We show that assuming $\mathsf{ZF}+\mathsf{AD}^+ +$ "$V = \mathrm{L} \bigl(\wp (\mathbb{R})\bigr)$", any poset which increases $\Theta$ does not preserve the truth of $\mathsf{AD}$. We also show that in $\mathsf{ZF} + \mathsf{AD}$, any…
We investigate abstract model theoretic properties which holds for models in which a truth or satisfaction predicate for a sublanguage of the signature is definable. We analyse in which cases those properties in fact ensure the definability…
This paper studies logical aspects of the notion of better quasi order, which has been introduced by C. Nash-Williams (Mathematical Proceedings of the Cambridge Philosophical Society 1965 & 1968). A central tool in the theory of better…
This is a lecture notes for a mini-course in Department of Mathematics, Ghent University, 14 Mar.-25 Mar. 2023.
We investigate modal logical aspects of provability predicates $\mathrm{Pr}_T(x)$ satisfying the following condition: $\mathbf{M}$: If $T \vdash \varphi \to \psi$, then $T \vdash \mathrm{Pr}_T(\ulcorner \varphi \urcorner) \to…
Bealer's intensional logics T1 and T2 were proposed and expounded most fully in his book \emph{Quality and Concept} (1982) \cite{QC} as well in \cite{C}. These logics are unique in being extensions of classical first-order associated to a…
Denote by Id$_c G$ the lattice of all principal $\ell$-ideals of an Abelian $\ell$-group $G$. Our main result is the following. Theorem. For every countable Abelian $\ell$-group $G$, every countable completely normal distributive 0-lattice…
Using recent results in topos theory, two systems of higher-order logic are shown to be complete with respect to sheaf models over topological spaces---so-called ``topological semantics''. The first is classical higher-order logic, with…
In this paper, several generalizations of the classical Halpern-L\"{a}uchli Theorem are proven for Marczewski and Ellentuck structures using only combinatorial methods.