12 citations · 49 across the 35 of their papers we have counts for
44 papers · 1 filter
Compactness phenomena in HOD and the Optimality of Magidor's Covering theorem
Tom Benhamou, James Cummings, Yair Hayut +2
We continue the study of compactness phenomena between the set-theoretic universe and initiated by Goldberg--Poveda \cite{GolPov}. We focus on compactness phenomena…
More notions of forcing add a square
Yair Hayut, Assaf Rinot, Zhixing You
Foreman and Magidor showed that the continuum hypothesis implies the existence of a countably-closed -cc forcing notion for adding . Here,…
The directedness of the Rudin-Keisler order at measurable cardinals
Yair Hayut, Alejandro Poveda
The manuscript is concerned with the Rudin-Keisler order of ultrafilters on measurable cardinals. The main theorem proved read as follows: Given regular cardinals , the fo…
The tree property on long intervals of regular cardinals
James Cummings, Yair Hayut, Menachem Magidor +3
In this paper we prove that the tree property can hold on regular cardinals in an interval which overlaps a strong limit cardinal. This is a crucial milestone in the long term proj…
Isomorphism Classes of Generating Sets
Tom Benhamou, James Cummings, Gabriel Goldberg +2
We introduce a new class of ultrafilters which generalizes the well-known class of simple -point ultrafilters. We prove that for any well-founded -directed partial order $\ma…
On a problem of Erdos and Hajnal
Shimon Garti, Yair Hayut, Saharon Shelah
We address a question of Erdős and Hajnal about the ordinary partition relation . For , assuming $2^λ=λ…
Dense ideals
Monroe Eskew, Yair Hayut
In this paper, we obtain the consistency, relative to large cardinals, of the existence of dense ideals on every successor of a regular cardinal simultaneously. Using a consequent…
Intermediate models with deep failure of choice
Yair Hayut, Assaf Shani
The following question was asked by Grigorieff: Suppose is a ZFC model and is a set-generic extension of . Can there be a ZF model so that $V\subset N \subset V[G…
The first measurable can be the first inaccessible cardinal
Moti Gitik, Yair Hayut, Asaf Karagila
In [8] the second and third authors showed that if the least inaccessible cardinal is the least measurable cardinal, then there is an inner model with . In this paper we…
Sealed Kurepa Trees
Itamar Giron, Yair Hayut
In this paper we investigate the problem of the distributivity of Kurepa trees. We show that it is consistent that there are Kurepa trees and for every Kurepa tree there is a small…
Prikry type forcings and the Bukovský-Dehornoy phenomena
Yair Hayut
This paper is meant to present in a coherent way several instances of quite common phenomena that was first identified (independently) by Bukovský and Dehornoy. We present the basi…
The Spectra of transitive models
Eilon Bilinsky, Yair Hayut
In this paper we study the spectrum of heights of transitive models of theories extending , under various definitions. In particular, we investigate the consistency stren…
Small measurable cardinals
Yair Hayut, Asaf Karagila
We continue the work from [8] and make a small -- but significant -- improvement to the definition of -decomposable system. This provides us with a better lifting of elementary…
The Gluing Property
Yair Hayut, Alejandro Poveda
We introduce a new compactness principle which we call the gluing property. For a measurable cardinal and a cardinal , we say that has the -gluing property if every s…
The Variety of Projection of a Tree-Prikry Forcing
Tom Benhamou, Moti Gitik, Yair Hayut
We study which -distributive forcing notions of size can be embedded into tree Prikry forcing notions with -complete ultrafilters under various large cardinal assumptions…
Mutually embeddable models of ZFC
Monroe Eskew, Sy-David Friedman, Yair Hayut +1
We investigate systems of transitive models of ZFC which are elementarily embeddable into each other and the influence of definability properties on such systems.
Subcompact cardinals, type omission and ladder systems
Yair Hayut, Menachem Magidor
We provide a model theoretical and tree property like characterization of --subcompactness and supercompactness. We explore the behaviour of those combinatorial principle…
On -Strongly Measurable Cardinals
Omer Ben-Neria, Yair Hayut
We prove several consistency results concerning the notion of -strongly measurable cardinal in HOD. In particular, we show that is it consistent, relative to a large cardinal hy…
A note on the normal filters extension property
Yair Hayut
We show that if and every normal filter on can be extended to a -complete ultrafilter then so does every -complete filter on . This answers a question…
Perfect Subtree Property for Weakly Compact Cardinals
Yair Hayut, Sandra Müller
We investigate the consistency strength of the statement: is weakly compact and there is no tree on with exactly many branches. We show that this statement fails st…
Dowker filters and Magidor forcing
Shimon Garti, Yair Hayut
We prove that the consistency of the existence of a Dowker filter at along with where is regular and uncountable. Using Magidor forcing we also prove the consis…
Stationary Reflection and the failure of SCH
Omer Ben-Neria, Yair Hayut, Spencer Unger
In this paper we prove that from large cardinals it is consistent that there is a singular strong limit cardinal such that the singular cardinal hypothesis fails at and eve…
Identity crises between supercompactness and Vopenka's Principle
Yair Hayut, Menachem Magidor, Alejandro Poveda
In this paper we study the notion of -supercompactness introduced by Bagaria in \cite{Bag} and prove the identity crises phenomenon for such class. Specifically, we show t…
Global Chang's Conjecture and singular cardinals
Monroe Eskew, Yair Hayut
We investigate the possibilities of global versions of Chang's Conjecture that involve singular cardinals. We show some limitations on such principles, and prove rel…