Related papers: Bar recursion in classical realisability : depende…
In this paper we study a new approach to classify mathematical theorems according to their computational content. Basically, we are asking the question which theorems can be continuously or computably transferred into each other? For this…
In \cite{Ca2016} and \cite{Ca2018}, we introduced a notion of effective reducibility between set-theoretical $\Pi_{2}$-statements; in \cite{Ca2025}, this was extended to statements of arbitrary (potentially even infinite) quantifier…
Brouwer-operations, also known as inductively defined neighbourhood functions, provide a good notion of continuity on Baire space which naturally extends that of uniform continuity on Cantor space. In this paper, we introduce a continuity…
Counters that hold natural numbers are ubiquitous in modeling and verifying software systems; for example, they model dynamic creation and use of resources in concurrent programs. Unfortunately, such discrete counters often lead to…
Explanations of the replication crisis often emphasize misconduct, questionable research practices, or incentive misalignment, implying that behavioral reform is sufficient. This paper argues that a substantial component is architectural:…
We propose a presentation of classical propositional tableaux elaborated by application of methods that are noteworthy in program design, namely program derivation with separation of concerns. We start by deriving from a straightforward…
Linearisability is a central notion for verifying concurrent libraries: a given library is proven safe if its operational history can be rearranged into a new sequential one which, in addition, satisfies a given specification.…
The first step in the formulation and study of the Riemann Hypothesis is the analytic continuation of the Riemann Zeta Function (RZF) in the full Complex Plane with a pole at $s=1$. In the current work, we study the analytic continuation of…
A common assumption in modern microeconomic theory is that choice should be rationalizable via a binary preference relation, which \citeauthor{Sen71a} showed to be equivalent to two consistency conditions, namely $\alpha$ (contraction) and…
We proved in a previous article that the bar complex of an E-infinity algebra inherits a natural E-infinity algebra structure. As a consequence, a well-defined iterated bar construction B^n(A) can be associated to any algebra over an…
Kolmogorovs axiomatic framework is the best-known approach to describing probabilities and, due to its use of the Lebesgue integral, leads to remarkably strong continuity properties. However, it relies on the specification of a probability…
Computational reflection allows us to turn verified decision procedures into efficient automated reasoning tools in proof assistants. The typical applications of such methodology include mathematical structures that have decidable theory…
Example-based guidance is widely used to improve mathematical reasoning at inference time, yet its effectiveness is highly unstable across problems and models-even when the guidance is correct and problem-relevant. We show that this…
The desirable gambles framework provides a rigorous foundation for imprecise probability theory but relies heavily on linear utility via its coherence axioms. In our related work, we introduced function-coherent gambles to accommodate…
In this dissertation we collect some results about "interactive realizability", a realizability semantics that extends the Brouwer-Heyting-Kolmogorov interpretation to (sub-)classical logic, more precisely to first-order intuitionistic…
The conformable derivative has been promoted in numerous publications as a new fractional derivative operator. This article provides a critical reassessment of this claim. We demonstrate that the conformable derivative is not a fractional…
We deal with relatives of GCH which are provable. In particular we deal with rank version of the revised GCH. Our motivation was to find such results when only weak versions of the axiom of choice are assumed but some of the results gives…
Fairly deep results of Zermelo-Frenkel (ZF) set theory have been mechanized using the proof assistant Isabelle. The results concern cardinal arithmetic and the Axiom of Choice (AC). A key result about cardinal multiplication is K*K = K,…
In this paper we investigate the question: 'How can A Foundational Classical Singlesuccedent Sequent Calculus be formulated?' The choice of this particular area of proof-theoretic study is based on a particular ground that is, to formulate…
Recursive analysis was introduced by A. Turing [1936], A. Grzegorczyk [1955], and D. Lacombe [1955]. It is based on a discrete mechanical framework that can be used to model computation over the real numbers. In this context the…