Related papers: The method of forcing
Typically, set theorists reason about forcing constructions in the context of ZFC. We show that without AC, several simple properties of forcing posets fail to hold, one of which answers Miller's question from arXiv:0704.3998.
This is an overview about a method of constructing ccc forcings: Suppose first that a continuous, commutative system of complete embeddings between countable forcings indexed along $\omega_1$ is given. Then its direct limit satisfies ccc by…
This paper presents a simple decidable logic of functional dependence LFD, based on an extension of classical propositional logic with dependence atoms plus dependence quantifiers treated as modalities, within the setting of generalized…
We introduce an iteration of forcing notions satisfying the countable chain condition with minimal damage to a strong coloring. Applying this method, we prove that Martin's axiom is strictly stronger than its restriction to forcing notions…
This thesis is concerned with investigations into the "complexity of term rewriting systems". Moreover the majority of the presented work deals with the "automation" of such a complexity analysis. The aim of this introduction is to present…
The aim of this work is to show how we can decompose a module (if decomposable) into an indecomposable module with the help of the minimization process.
Category theory provides a powerful tool to organize mathematics. A sample of this descriptive power is given by the categorical analysis of the practice of "classes as shorthands" in ZF set theory. In this case category theory provides a…
The methodology used here might provide a neat method of examining paradoxes and ways to circumvent them. Most of the known set theoretic paradoxes (Russell's, Cantor's, Burali-Forti's,..) can be paralleled here and examined. This account…
Mechanical reasoning is a key area of research that lies at the crossroads of mathematical logic and artificial intelligence. The main aim to develop mechanical reasoning systems (also known as theorem provers) was to enable mathematicians…
Taking symmetric extensions can be considered as a generalisation of forcing, which produces a richer multiverse of models with and without the axiom of choice. We can study the structure of this multiverse using modal logic. In particular,…
We present a prototype of an integrated reasoning environment for educational purposes. The presented tool is a fragment of a proof assistant and automated theorem prover. We describe the existing and planned functionality of the theorem…
In this paper, we shall prove the Chung-Feller Theorem in several ways. We provide an inductive proof, bijective proof, and proofs using generating functions, and the Cycle Lemma of Dvoretzky and Motzkin.
We give a short introduction to category theory aimed at philosophers. We emphasize methodological issues and philosophical ramifications.
The motivation for this paper comes out of our experience with teaching natural deduction (ND) and with the way this formal system is implemented by the \textsc{Coq} proof assistant, namely by means of so-called tactics, which are…
We propose FC, a new logic on words that combines finite model theory with the theory of concatenation - a first-order logic that is based on word equations. Like the theory of concatenation, FC is built around word equations; in contrast…
While proof is a central component of postsecondary mathematical study, proof construction has historically posed significant difficulties for students who intend to earn mathematics degrees at the undergraduate level. This work is…
By a virtual model, we mean a model of set theory which is elementary in its transitive closure. Virtual models are first used by Neeman \cite{neeman2014forcing} to iterate forcing. That paper is concerned with proper forcing. The method…
While model checking has often been considered as a practical alternative to building formal proofs, we argue here that the theory of sequent calculus proofs can be used to provide an appealing foundation for model checking. Since the…
We propose Equivariant ZFA with Choice as a foundation for nominal techniques that is stronger than ZFC and weaker than FM, and why this may be particularly helpful in the context of automated reasoning.
Automating the fact checking (FC) process relies on information obtained from external sources. In this work, we posit that it is crucial for FC models to make veracity predictions only when there is sufficient evidence and otherwise…