Related papers: The uniqueness of elementary embeddings
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…
Normal ideals on regular uncountable cardinals are familiar objects. We investigate ideals that are pleasant--while a normal ideal is closed under arbitrary diagonal unions, a pleasant ideal is closed only under diagonal unions indexed by…
This report presents an expression for the number of a multiset's sub-multisets of a given cardinality as a function of the multiplicity of its elements. This is also the number of distinct samples of a given size that may be produced by…
Several machine learning models are defined for inputs of any size, such as graphs with different numbers of nodes and point clouds containing varying numbers of points. The universality properties of such any-dimensional models remain…
We calculate the number of unary clones (submonoids of the full transformation monoid) containing the permutations, on an infinite base set. It turns out that this number is quite large, on some cardinals as large as the whole clone…
We consider a generalization of the interior Schwarzschild solution that we match to the exterior one to build global C^1 models that can have arbitrary large mass, or density, with arbitrary size. This is possible because of a new insight…
We introduce combinatorial principles that characterize strong compactness and supercompactness for inaccessible cardinals but also make sense for successor cardinals. Their consistency is established from what is supposedly optimal.…
In this paper, we have established boundaries of cardinal numbers of nonempty sets in finite non-$T_1$ topological spaces using interval analysis. For a finite set with known cardinality, we give interval estimations based on the closure…
We investigate an extension of ZFC set theory (in an extended language) that stipulates the existence of a proper class of indiscernibles over the universe. One of the main results of the paper shows that the purely set-theoretical…
In this paper we develop in detail the geometric constructions that lead to many uniqueness results for the determination of polyhedral sets, typically scatterers, by a finite minimal number of measurements. We highlight how unique…
Cardinal characteristics of the continuum represent the boundaries in size between the countable and the continuum with respect to certain properties of sets. They are often defined as the minimum sizes of families of reals that meet some…
We study the influence of the existence of large cardinals on the existence of wellorderings of power sets of infinite cardinals $\kappa$ with the property that the collection of all initial segments of the wellordering is definable by a…
Embedding theorems have continued to be a topic of interest in the general theory of relativity since these help connect the classical theory to higher-dimensional manifolds. This paper deals with spacetimes of embedding class one, i.e.,…
An inner model M is MINIMAL if there is a class A such that <M,A> is amenable yet has no transitive proper elementary submodel. We study minimal universes in the context of 0#. For example we prove: If 0# exists then there is an inner model…
We investigate systems of transitive models of ZFC which are elementarily embeddable into each other and the influence of definability properties on such systems.
We study cofinal systems of finite subsets of $\omega_1$. We show that while such systems can be NIP, they cannot be defined in an NIP structure. We deduce a positive answer to a question of Chernikov and Simon from 2013: in an NIP theory,…
Accessible categories admit a purely category-theoretic replacement for cardinality: the internal size. Generalizing results and methods from arXiv:1708.06782, we examine set-theoretic problems related to internal sizes and prove several…
We show that some of the most prominent large cardinal notions can be characterized through the validity of certain combinatorial principles at $\omega_2$ in forcing extensions by the pure side condition forcing introduced by Neeman. The…
We mainly investigate model of set theory with restricted choice, e.g., ZF + DC + "the family of countable subsets of lambda is well ordered for every lambda" (really local version for a given lambda). In this frame much of pcf theory can…
This paper describes problems concerning the range of cardinalities of sumsets and restricted sumsets of finite subsets of the integers and finite subsets of ordered abelian groups.