Related papers: Strong Rigidity and Elementary Embeddings
The theory ZFC implies the scheme that for every cardinal $\delta$ we can make $\delta$ many dependent choices over any definable relation without terminal nodes. Friedman, the first author, and Kanovei constructed a model of ZFC$^-$ (ZFC…
Tight and essentially tight modules generalize weakly injective modules. Essential tightness requires embeddings to be essential. This restriction makes the two notions totally different. In this note, we investigate cases when those two…
We prove a result concerning elementary embeddings of the set-theoretic universe into itself (Reinhardt embeddings) and functions on ordinals that "eventually dominate" such embeddings. We apply that result to show the existence of…
The following pcf results are proved: 1. Assume that kappa > aleph_0 is a weakly compact cardinal. Let mu > 2^kappa be a singular cardinal of cofinality kappa. Then for every regular lambda < pp^+_{Gamma(kappa)} (mu) there is an increasing…
In this article we obtain a fundamental measure functional for the model of aligned hard hexagons in the plane. Our aim is not just to provide a functional for a new, admittedly academic, model, but to investigate the structure of…
We lower substantially the strength of the assumptions needed for the validity of certain results in category theory and homotopy theory which were known to follow from Vopenka's principle. We prove that the necessary large-cardinal…
A proof will be presented that the existence of a non-trivial $\Sigma_1$-elementary embedding $j: V_{\lambda+3} \prec V_{\lambda+3}$ is inconsistent with $\textsf{ZF}$. Sections 1 and 2 shall review various important contributions from the…
In this paper, the template will be developed from an assumed Stress Method, which its formulation is based on the Hellinger-Reissner principle developed according to Kang's study in 1986. The element stiffness is decomposed into a basic…
We give a method for constructing (possible large) self--small modules via some special homomorphisms of rings, called here weak epimorphisms.
Conventional word embeddings represent words with fixed vectors, which are usually trained based on co-occurrence patterns among words. In doing so, however, the power of such representations is limited, where the same word might be…
We provide a self-contained introduction to the classical theory of universal-homogeneous models (also known as generic structures, rich models, or Fra\"iss\'e limits). In the literature, most treatments restrict consideration to embeddings…
Low-dimensional embeddings are a cornerstone in the modelling and analysis of complex networks. However, most existing approaches for mining network embedding spaces rely on computationally intensive machine learning systems to facilitate…
We extend and improve the result of Makkai and Par\'e that the powerful image of any accessible functor F is accessible, assuming there exists a sufficiently large strongly compact cardinal. We reduce the required large cardinal assumption…
The effective lattice models in strongly correlated electron systems are \emph{derived} in particular for the cuprate superconductors, that incorporate the quantum fluctuations of the spin Berry's phase and the antiferromagnetic…
We prove a rigidity theorem that shows that, under many circumstances, quasi-isometric embeddings of equal rank, higher rank symmetric spaces are close to isometric embeddings. We also produce some surprising examples of quasi-isometric…
We consider a perturbation $f$ of a hyperbolic toral automorphism $L$. We study rigidity related to exceptional properties of the strong and weak stable foliations for $f$. If the strong foliation is mapped to the linear one by the…
We introduce the notion of $\lambda$-equivalence and $\lambda$-embeddings of objects in suitable categories. This notion specializes to $L_{\infty\lambda}$-equivalence and $L_{\infty\lambda}$-elementary embedding for categories of…
A methodology on making the variational principle well-posed in degenerate systems is constructed. In the systems including higher-order time derivative terms being compatible with Newtonian dynamics, we show that a set of position…
We consider special quantum systems containing both distinguishable and identical constituents. It is shown that for these systems the Freudenthal construction based on cubic Jordan algebras naturally defines entanglement measures invariant…
This is the first in a series of papers in which we construct and study a new $p$-adic cohomology theory for varieties over Laurent series fields $k(\!(t)\!)$ in characteristic $p$. This will be a version of rigid cohomology, taking values…