Related papers: Properties of Norms on Sets
We study variants of classical Laver forcing defined from co-ideals and analyze their combinatorial properties in terms of the Kat\v{e}tov order. In particular, we give a Kat\v{e}tov-theoretic characterization of when Laver forcing…
A combinatorial object representing schemas of, possibly skew, perspectives, called {\em a configuration of skew perspective} has been defined in \cite{klik:binom}, \cite{maszko}. Here we develop the theory of configurations generalizing…
The technique of symmetric extensions is derived from forcing and it is one of the most important tools for studying models without the Axiom of Choice. Despite being incredibly successful since the 1960s, our understanding of the technique…
Tarski gave a general semantics for deductive reasoning: a formula a may be deduced from a set A of formulas iff a holds in all models in which each of the elements of A holds. A more liberal semantics has been considered: a formula a may…
The forcing method is a powerful tool to prove the consistency of set-theoretic assertions relative to the consistency of the axioms of set theory. Laver's theorem and Bukovsk\'y's theorem assert that set-generic extensions of a given…
Based on the work of Shelah, Kellner, and T\u{a}nasie (Fund. Math., 166(1-2):109-136, 2000 and Comment. Math. Univ. Carolin., 60(1):61-95, 2019), and the recent developments in the third author's master's thesis, we develop a general theory…
We investigate the possibility of modelling the syntax and semantics of natural language by constraints, or rules, imposed by the multi-dimensional type theory Nabla. The only multiplicity we explicitly consider is two, namely one dimension…
The process of cognition is analysed to adjust the set theory to physical description. Postulates and basic definitions are revised. The specific sets of predicates, called presets, corresponding to the physical objects identified by an…
Given a countable model of set theory, we study the structure of its generic multiverse, the collection of its forcing extensions and ground models, ordered by inclusion. Mostowski showed that any finite poset embeds into the generic…
We synthesize and unify notions of regularity, both of individual sets and of collections of sets, as they appear in the convergence theory of projection methods for consistent feasibility problems. Several new characterizations of…
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…
A core aspect of compositionality, systematicity is a desirable property in ML models as it enables strong generalization to novel contexts. This has led to numerous studies proposing benchmarks to assess systematic generalization, as well…
While most social norms are informal, they are often formalized by companies in contracts to regulate trades of goods and services. When poorly written, contracts may contain normative conflicts resulting from opposing deontic meanings or…
In many situations, the decision maker observes items in sequence and needs to determine whether or not to retain a particular item immediately after it is observed. Any decision rule creates a set of items that are selected. We consider…
A paper of the first author and Zilke proposed seven combinatorial problems around formulas for the characteristic polynomial and the exponents of an isolated quasihomogeneous singularity. The most important of them was a conjecture on the…
We bring forward a logical system of transition algebras that enhances many-sorted first-order logic using features from dynamic logics. The sentences we consider include compositions, unions, and transitive closures of transition…
In general proof theory there are two approaches to the question of identity criteria for proofs. The first approach, which stems from Prawitz, Kreisel and Lambek, and is based on normalization of proofs, gives good results in…
Forcing axioms are generalizations of Baire category principles that allow one to intersect more dense open sets and to do so in a wider variety of circumstances. In this paper we introduce two new forcing axioms related to posets which…
This is an introduction to the set-theoretic method of forcing, including its application in proving the independence of the Continuum Hypothesis from the Zermelo-Fraenkel axioms of set theory. I presuppose no particular mathematical…
Using standard methods (due to Janson, Stein-Chen, and Talagrand) from probabilistic combinatorics, we explore the following general theme: As one progresses from each member of a family of objects ${\cal A}$ being "covered" by at most one…