相关论文: The combinatorics of reasonable ultrafilters
This paper introduces a reformulation of the classical convergence theorem for spectral sequences of filtered complexes which provides an algorithm to effectively compute the induced filtration on the total (co)homology, as soon as the…
This paper continues the study of the Ramsey-like large cardinals. Ramsey-like cardinals are defined by generalizing the characterization of Ramsey cardinals via the existence of elementary embeddings. Ultrafilters derived from such…
Algebras of ultradifferentiable generalized functions are introduced. We give a microlocal analysis within these algebras related to the regularity type and the ultradifferentiable property.
In this article, we define the notion of a filtration and then give the basic theorems on initial and progressive enlargements of filtrations.
Superfilters are generalized ultrafilters, which capture the underlying concept in Ramsey theoretic theorems such as van der Waerden's Theorem. We establish several properties of superfilters, which generalize both Ramsey's Theorem and its…
We show relative to strong hypotheses that patterns of compact cardinals in the universe, where a compact cardinal is one which is either strongly compact or supercompact, can be virtually arbitrary. Specifically, we prove if V is a model…
An infinite cardinal $\lambda$ is called Fr\'echet if the Fr\'echet filter on $\lambda$ extends to a countably complete ultrafilter. We investigate the relationship between Fr\'echet cardinals and strongly compact cardinals under a…
This short article contains the construction of a construction that generalizes the concept of the derivative of a function of one variable, using the theory of filters. The paper presents a new concept, demonstrates that it really…
The main result of this paper is a partial answer to [math.LO/9909115, Problem 5.5]: a finite iteration of Universal Meager forcing notions adds generic filters for many forcing notions determined by universality parameters. We also give…
We lay the combinatorial foundations for [ShSt:340] by setting up and proving the essential properties of the coding apparatus for singular cardinals. We also prove another result concerning the coding apparatus for inaccessible cardinals.
We give a model-theoretic perspective on regular ultrafilter construction in the twentieth and twenty-first century (so far), and explain the "canonical Boolean algebra" recently developed by Malliaris and Shelah.
We like to develop model theory for $T$, a complete theory in $\mathbb{L}_{\theta,\theta}(\tau)$ when $\theta$ is a compact cardinal. By [Sh:300a] we have bare bones stability and it seemed we can go no further. Dealing with ultrapowers…
We prove the consistency of ``CH + 2^{aleph_1} is arbitrarily large + 2^{aleph_1} not-> (omega_1 x omega)^2_2''. If fact, we can get 2^{aleph_1} not-> [omega_1 x omega]^2_{aleph_0}. In addition to this theorem, we give generalizations to…
Tunable filters are set to revolutionize many aspects of experimental astrophysics, particularly for applications in observational cosmology. After a summary of the fundamentals of classical spectroscopy, we present a review of the current…
In this paper we analyze the connection between some properties of partially strongly compact cardinals: the completion of filters of certain size and instances of the compactness of $\mathcal{L}_{\kappa,\kappa}$. Using this equivalence we…
We continue the exploration of various aspects of divisibility of ultrafilters, adding one more relation to the picture: multiplicative finite embeddability. We show that it lies between divisibility relations $\mid_M$ and…
In this note, our goal is to describe the concept of generalized derivations in the context of BiHom-supertrialgebras. We provide a comprehensive analysis of the properties and applications of these generalized derivations, including their…
The aim of this paper is to construct ultrafilters without immediate predecessors in the Rudin-Frolik order in $\beta \kappa\setminus \kappa$, where $\kappa$ is a regular cardinal. This generalizes the problem posed by Peter Simon more than…
We provide sufficient conditions for systems of polynomial equations over general (real or complex) algebras to have a solution. This generalizes known results on quaternions, octonions and matrix algebras. We also generalize the…
We construct a model of the form $L[A,U]$ that exhibits the simplest structural behavior of $\sigma$-complete ultrafilters in a model of set theory with a single measurable cardinal $\kappa$ , yet satisfies $2^\kappa = \kappa^{++}$. This…