相关论文: Club guessing and the universal models

The goal of the article is to better understand cosupport in triangulated categories since it is still quite mysterious. We study boundedness of local cohomology and local homology functors using Koszul objects, give some characterizations…

After the publication of [J. Algebra 638 (2024) 625-669], we noticed a serious mistake in the treatment of the partition algebra. In particular, we assumed in the proof of Lemma 4.9 that the trivial P_n-module is indexed by the empty set…

New proposals for causal discovery algorithms are typically evaluated using simulations and a few selected real data examples with known data generating mechanisms. However, there does not exist a general guideline for how such evaluation…

Linear sets over finite fields are central objects in finite geometry and coding theory, with deep connections to structures such as semifields, blocking sets, KM-arcs, and rank-metric codes. Among them, $i$-clubs, a class of linear sets…

We study combinatorial principles known as stick and club. Several variants of these principles and cardinal invariants connected to them are also considered. We introduce a new kind of side-by-side product of partial orders which we call…

We give an elementary construction of a $p\geq 1$-singular Gelfand-Tsetlin $\mathfrak{gl}_n(\mathbb C)$-module in terms of local distributions. This is a generalization of the universal $1$-singular Gelfand-Tsetlin $\mathfrak{gl}_n(\mathbb…

We define a countable antichain condition (ccc) property for partial orderings, weaker than precalibre-$\aleph_1$, and show that Martin's axiom restricted to the class of partial orderings that have the property does not imply Martin's…

We deal with the existence of universal members in a given cardinality for several classes. First we deal with classes of Abelian groups, specifically with the existence of universal members in cardinalities which are strong limit singular…

Justin Moore's weak club-guessing principle $\mho$ admits various possible generalizations to the second uncountable cardinal. One of them was shown to hold in ZFC by Shelah. A stronger one was shown to follow from several consequences of…

We begin by recalling the essentially global character of universes in various models of homotopy type theory, which prevents a straightforward axiomatization of their properties using the internal language of the presheaf toposes from…

In this letter we summarize some recent theoretical work on the design of collectives, i.e., of systems containing many agents, each of which can be viewed as trying to maximize an associated private utility, where there is also a world…

Generalized numberings are an extension of Ershov's notion of numbering, based on partial combinatory algebra (pca) instead of the natural numbers. We study various algebraic properties of generalized numberings, relating properties of the…

We make use of generalized iterations of Jensen forcing to define a cardinal-preserving generic model of ZF for any $n\ge 1$ and each of the following four Choice hypotheses: (1)…

Over the past decades, researchers and ML practitioners have come up with better and better ways to build, understand and improve the quality of ML models, but mostly under the key assumption that the training data is distributed…

Inference of community structure in probabilistic graphical models may not be consistent with fairness constraints when nodes have demographic attributes. Certain demographics may be over-represented in some detected communities and…

We study the complexity of the classification problem for countable models of set theory (ZFC). We prove that the classification of arbitrary countable models of ZFC is Borel complete, meaning that it is as complex as it can conceivably be.…

This paper is an expanded version of two talks given by the author at the Summer School on the Interactions between Homotopy Theory and Algebra at the University of Chicago, July 26 to August 6, 2004. It describes a connection between model…

We introduce a new model of collective decision making, when a global decision needs to be made but the parties only possess partial information, and are unwilling (or unable) to first create a globalcomposite of their local views. Our…

Compositional generalization benchmarks for semantic parsing seek to assess whether models can accurately compute meanings for novel sentences, but operationalize this in terms of logical form (LF) prediction. This raises the concern that…

We study the globalization of partial actions on sets and topological spaces and of partial coactions on algebras by applying the general theory of globalization for geometric partial comodules, as previously developed by the authors. We…