Related papers: Strong Rigidity and Elementary Embeddings

The rigid relation principle, introduced in this article, asserts that every set admits a rigid binary relation. This follows from the axiom of choice, because well-orders are rigid, but we prove that it is neither equivalent to the axiom…

We investigate large set axioms defined in terms of elementary embeddings over constructive set theories, focusing on $\mathsf{IKP}$ and $\mathsf{CZF}$. Most previously studied large set axioms, notably the constructive analogues of large…

One of the numerous characterizations of a Ramsey cardinal kappa involves the existence of certain types of elementary embeddings for transitive sets of size \kappa satisfying a large fragment of ZFC. We introduce new large cardinal axioms…

We study Structural Reflection beyond Vop\v{e}nka's Principle, at the level of almost-huge cardinals and higher, up to rank-into-rank embeddings. We identify and classify new large cardinal notions in that region that correspond to some…

We give a sharper version of a theorem of Rosicky, Trnkova and Adamek, and a new proof of a theorem of Rosicky, both about colimit preservation between categories of structures. Unlike the original proofs, which use category-theoretic…

We study general methods to build forking-like notions in the framework of tame abstract elementary classes (AECs) with amalgamation. We show that whenever such classes are categorical in a high-enough cardinal, they admit a good frame: a…

In statistical relational learning, the link prediction problem is key to automatically understand the structure of large knowledge bases. As in previous studies, we propose to solve this problem through latent factorization. However, here…

Assume ZF (without the Axiom of Choice). Let $j:V_\varepsilon\to V_\delta$ be a non-trivial $\in$-cofinal $\Sigma_1$-elementary embedding, where $\varepsilon,\delta$ are limit ordinals. We prove some restrictions on the constructibility of…

We prove a universal embedding theorem for flag manifolds: every flag manifold admits a holomorphic isometric embedding into an irreducible classical flag manifold. This result generalizes the classical celebrated embedding theorems of…

A theoretical development is carried to establish fundamental results about rank-initial embeddings and automorphisms of countable non-standard models of set theory, with a keen eye for their sets of fixed points. These results are then…

Let A be a commutative ring, B a commutative A-algebra and M a complex of B-modules. We begin by constructing the square Sq_{B/A} M, which is also a complex of B-modules. The squaring operation is a quadratic functor, and its construction…

We deal with the random combinatorial structures called assemblies. By weakening the logarithmic condition which assures regularity of the number of components of a given order, we extend the notion of logarithmic assemblies. Using the…

We introduce the theory of strong homotopy types of simplicial complexes. Similarly to classical simple homotopy theory, the strong homotopy types can be described by elementary moves. An elementary move in this setting is called a strong…

We introduce the notion of a critical cardinal as the critical point of sufficiently strong elementary embedding between transitive sets. Assuming the axiom of choice this is equivalent to measurability, but it is well-known that choice is…

A cardinal is weakly Reinhardt if it is the critical point of an elementary embedding from the universe of sets into a model that contains the double powerset of every ordinal. This note establishes the equiconsistency of a proper class of…

Rigid, cage-like molecules, like diamondoids, show unique self-assembly behavior, such as templating 1-D nanomaterial assembly via pathways that are typically blocked for such bulky substituents. We investigate molecular forces between…

Building on work of Holy, L\"ucke and Njegomir \cite{MR3913154} on small embedding characterizations of large cardinals, we use some classical results of Baumgartner (see \cite{MR0384553} and \cite{MR0540770}), to give characterizations of…

We provide a new criterion for embedding $\mathbb{E}_{0}$, and apply it to equivalence relations in model theory. This generalize the results of the authors and Pierre Simon on the Borel cardinality of Lascar strong types equality, and…

Hayut and first author isolated the notion of a critical cardinal in [1]. In this work we answer several questions raised in the original paper. We show that it is consistent for a critical cardinals to not have any ultrapower elementary…

On every set A there is a rigid binary relation, i.e. such a relation R that there is no homomorphism (A,R)->(A,R) except the identity (Vopenka et al. [1965]). We state two conjectures which strengthen this theorem. We prove these…