Related papers: Lords of the iteration
This paper presents the main results in my Ph.D. thesis. In what follows several proofs of SCH are presented introducing a family of covering properties which implies both SCH and the failure of various forms of square. These covering…
This paper from 2008 is the first in a series of three related papers on modal methods in interpretability logics and applications. In this first paper the foundations are laid for later results. These foundations consist of a thorough…
In this thesis new objects to the existing set of invariants of Lie algebras are added. These invariant characteristics are capable of describing the nilpotent parametric continuum of Lie algebras. The properties of these invariants, in…
We get a quite maximal version of the colouring property $Pr_1$ by proving $Pr_1(\lambda,\lambda,\lambda,\theta)$ when $\lambda = \partial^+, \partial > \theta$ are regular cardinals.
We lay the ground for an Isabelle/ZF formalization of Cohen's technique of forcing. We formalize the definition of forcing notions as preorders with top, dense subsets, and generic filters. We formalize the definition of forcing notions as…
We study principles of the form: if a name $\sigma$ is forced to have a certain property $\varphi$, then there is a ground model filter $g$ such that $\sigma^g$ satisfies $\varphi$. We prove a general correspondence connecting these name…
For a relational structure ${\mathbb X}$ we investigate the partial order $\langle {\mathbb P} ({\mathbb X}) ,\subset \rangle$, where ${\mathbb P} ({\mathbb X}):=\{ f[X]: f\in \mathop{\rm Emb}\nolimits ({\mathbb X})\}$. Here we consider…
We show that several classes of ordered structures (namely, convex linear orders, layered permutations, and compositions) admit first-order logical limit laws.
We investigate the decidability of the monadic second-order (MSO) theory of the structure $\langle \mathbb{N};<,P_1, \ldots,P_d \rangle$, for various unary predicates $P_1,\ldots,P_d \subseteq \mathbb{N}$. We focus in particular on…
We present a calculus providing a Curry-Howard correspondence to classical logic represented in the sequent calculus with explicit structural rules, namely weakening and contraction. These structural rules introduce explicit erasure and…
The literature on judgment aggregation is moving from studying impossibility results regarding aggregation rules towards studying specific judgment aggregation rules. Here we give a structured list of most rules that have been proposed and…
Replication of experimental results has been a challenge faced by many scientific disciplines, including the field of machine learning. Recent work on the theory of machine learning has formalized replicability as the demand that an…
In this paper, we define a new realizability semantics for the simply typed lambda-mu-calculus. We show that if a term is typable, then it inhabits the interpretation of its type. We also prove a completeness result of our realizability…
A comparison of Landin's form of lambda calculus with Church's shows that, independently of the lambda calculus, there exists a mechanism for converting functions with arguments indexed by variables to the usual kind of function where the…
In this paper we provide a general tool to prove the consistency of $I1(\lambda)$ with various combinatorial properties at $\lambda$ typical at settings with $2^\lambda>\lambda^+$, that does not need a profound knowledge of the forcing…
We investigate two variants of splitting tree forcing, their ideals and regularity properties. We prove connections with other well-known notions, such as Lebesgue measurablility, Baire- and Doughnut-property and the Marczewski field.…
We introduce the notion of reflexivity for combinatory algebras. Reflexivity can be thought of as an equational counterpart of the Meyer-Scott axiom of combinatory models, which indeed allows us to characterise an equationally definable…
This paper develops an algorithmic-based approach for proving inductive properties of propositional sequent systems such as admissibility, invertibility, cut-elimination, and identity expansion. Although undecidable in general, these…
We develop a forcing framework based on the idea of amalgamating language fragments into a theory with a canonical term model. We then demonstrate the usefulness of this framework by applying it to variants of the extended Namba problem, as…
We present a different combinatorial interpretations of Lucas and Gibonacci numbers. Using these interpretations we prove several new identities, and simplify the proofs of several known identities. Some open problems are discussed towards…