Related papers: Choiceless Chain Conditions
A structural condition is given for finite maximal antichains in the homomorphism order of relational structures to have the splitting property. It turns out that non-splitting antichains appear only at the bottom of the order. Moreover, we…
We extend the theory of infinite-exponent partition relations to arbitrary linear order types, with a particular focus on the real number line. We give a complete classification of all consistent partition relations on the real line with…
We construct a special type of antichain (i. e., a family of subsets of a set, such that no subset is contained in another) using group-theoretical considerations, and obtain an upper bound on the cardinality of such an antichain. We apply…
We show that Morley's theorem on the number of countable models of a countable first-order theory becomes an undecidable statement when extended to second-order logic. More generally, we calculate the number of equivalence classes of…
This paper describes a process for clustering concepts into chains from data presented randomly to an evaluating system. There are a number of rules or guidelines that help the system to determine more accurately what concepts belong to a…
We study automatic sequences and automatic systems generated by general constant length (nonprimitive) substitutions. While an automatic system is typically uncountable, the set of automatic sequences is countable, implying that most…
Counterfactual inference is a powerful tool, capable of solving challenging problems in high-profile sectors. To perform counterfactual inference, one requires knowledge of the underlying causal mechanisms. However, causal mechanisms cannot…
We study selective and game-theoretic versions of properties like the ccc, weak Lindel\"ofness and separability, giving various characterizations of them and exploring connections between these properties and some classical cardinal…
The replacement (or collection or choice) axiom scheme asserts bounded quantifier exchange. We prove the independence of this scheme from various weak theories of arithmetic, sometimes under a complexity assumption.
In this article, we review selective inference, a set of techniques for inference when the statistical question asked is a function of the data. This setting often arises in contemporary scientific workflows, where hypotheses and parameters…
Mixed monotone systems form an important class of nonlinear systems that have recently received attention in the abstraction-based control design area. Slightly different definitions exist in the literature, and it remains a challenge to…
Many clustering schemes are defined by optimizing an objective function defined on the partitions of the underlying set of a finite metric space. In this paper, we construct a framework for studying what happens when we instead impose…
CZF is a system of set theory which, over classical logic, is equivalent to ZF, while over intuitionistic logic, it has a well-known constructive type-theoretic interpretation. This article introduces a simpler, intuitive family of…
Various theorems for the preservation of set-theoretic axioms under forcing are proved, regarding both forcing axioms and axioms true in the Levy-Collapse. These show in particular that certain applications of forcing axioms require to add…
Consider a difference equation which takes the k-th largest output of m functions of the previous m terms of the sequence. If the functions are also allowed to change periodically as the difference equation evolves this is analogous to a…
The central open question in Descriptive Complexity is whether there is a logic that characterizes deterministic polynomial time (PTIME) on relational structures. Towards this goal, we define a logic that is obtained from first-order logic…
Abstaining classifiers have the option to abstain from making predictions on inputs that they are unsure about. These classifiers are becoming increasingly popular in high-stakes decision-making problems, as they can withhold uncertain…
We introduce the idea of a coherent adequate set of models, which can be used as side conditions in forcing. As an application we define a forcing poset which adds a square sequence on $\omega_2$ using finite conditions.
Causal processes in nature may contain cycles, and real datasets may violate causal sufficiency as well as contain selection bias. No constraint-based causal discovery algorithm can currently handle cycles, latent variables and selection…
The union-closed sets conjecture (sometimes referred to as Frankl's conjecture) states that every finite, nontrivial union-closed family of sets has an element that is in at least half of its members. Although the conjecture is known to be…