相关论文: Club guessing and the universal models
Measuring says that for e\-very sequence $(C_\delta)_{\delta<\omega_1}$ with each $C_\delta$ being a closed subset of $\delta$ there is a club $C\subseteq\omega_1$ such that for every $\delta\in C$, a tail of $C\cap\delta$ is either…
In clustering problems, a central decision-maker is given a complete metric graph over vertices and must provide a clustering of vertices that minimizes some objective function. In fair clustering problems, vertices are endowed with a color…
In this paper, we unify the study of classical and non-classical algebra-valued models of set theory, by studying variations of the interpretation functions for identity and set-membership. Although, these variations coincide with the…
The Frankl's conjecture, formulated in 1979. and still open, states that in every family of sets closed for unions there is an element contained in at least half of the sets. A family Fc is called Frankl-complete (or FC-family) if in every…
In order to address complex systems, apply pattern recongnition on their evolution could play an key role to understand their dynamics. Global patterns are required to detect emergent concepts and trends, some of them with qualitative…
Uncovering the hidden regularities and organizational principles of networks arising in physical systems ranging from the molecular level to the scale of large communication infrastructures is the key issue for the understanding of their…
The paper uses the formalism of indexed categories to recover the proof of a standard final coalgebra theorem, thus showing existence of final coalgebras for a special class of functors on categories with finite limits and colimits. As an…
Many of the traditional recommendation algorithms are designed based on the fundamental idea of mining or learning correlative patterns from data to estimate the user-item correlative preference. However, pure correlative learning may lead…
We study criteria for a ring - or more generally, for a small category - to be Gorenstein and for a module over it to be of finite projective dimension. The goal is to unify the universal coefficient theorems found in the literature and to…
We generalize the small object argument in order to allow for its application to proper classes of maps (as opposed to sets of maps in Quillen's small object argument). The necessity of such a generalization arose with appearance of several…
The boolean elements of a Coxeter group have been characterized and shown to possess many interesting properties and applications. Here we introduce "prism permutations," a generalization of those elements, characterizing the prism…
In this article, we compare two different notions of partially defined group strutures, namely partial groups and pregroups, as introduced by Chermak and Stallings respectively. In particular we prove that the category of pregroups can be…
We continue to investigate club guessing (see [Sh:g, Ch III] and [Sh:e, Ch VI]), continuing Dzamonja and Shelah [DjSh:691]
In previous work, the authors introduced the notion of Q-Koszul algebras, as a tool to "model" module categories for semisimple algebraic groups over fields of large characteristics. Here we suggest the model extends to small…
We answer a question of Moore by building a forcing extension satisfying measuring together with CH. The construction works over any model of ZFC and can be described as a forcing iteration with countable structures as side conditions and…
We introduce a simple diagnostic test for assessing the overall or partial goodness of fit of a linear causal model with errors being independent of the covariates. In particular, we consider situations where hidden confounding is…
We observe that the notion of two sets being equal up to finitely many elements is a homotopy equivalence relation in a model category, and suggest a homotopy-invariant variant of Generalised Continuum Hypothesis about which more can be…
We show if we use countable support iteration of forcing notions not adding reals that satisfy additional conditions, then the limit forcing does not add reals. As a result we prove that we can amalgamate two earlier methods and prove the…
The Bristol model is an inner model of $L[c]$, where $c$ is a Cohen real, which is not constructible from a set. The idea was developed in 2011 in a workshop taking place in Bristol, but was only written in detail by the author in [8]. This…
Improving and clarifying a construction of Horowitz and Shelah, we show how to construct (in $\textsf{ZF}$, that is, without using the Axiom of Choice) maximal cofinitary groups. Among the groups we construct, one is definable by a formula…