Yair Hayut

activity

20152026

most citedOn the consistency of local and global versions of Chang's Conjecture

12 citations · 49 across the 35 of their papers we have counts for

collaborators

45 papers

math.LO2026

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 $HOD$ initiated by Goldberg--Poveda \cite{GolPov}. We focus on compactness phenomena…

math.LO2026

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 $ℵ_{2}$ -cc forcing notion $P$ for adding $□_{ℵ_{1}}$ . Here,…

math.LO2026

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 $λ \leq κ$ , the fo…

math.LO2025

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…

math.LO2025

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 $P$ -point ultrafilters. We prove that for any well-founded $σ$ -directed partial order $\ma…

math.LO2025

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 $ℵ_{ω + 1} ↛ (ℵ_{ω + 1}, (3)_{ℵ_{0}})^{2}$ . For $θ = cf (λ) < λ$ , assuming $2^λ=λ…

math.LO2024

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…

math.LO2024

Intermediate models with deep failure of choice

Yair Hayut, Assaf Shani

The following question was asked by Grigorieff: Suppose $V$ is a ZFC model and $V [G]$ is a set-generic extension of $V$ . Can there be a ZF model $N$ so that $V\subset N \subset V[G…

math.LO2024

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 $o (κ) \geq 2$ . In this paper we…

math.LO2023

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…

math.LO2023

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…

math.LO2023

The Spectra of transitive models

Eilon Bilinsky, Yair Hayut

In this paper we study the spectrum of heights of transitive models of theories extending $V = L [A]$ , under various definitions. In particular, we investigate the consistency stren…

math.LO2022

Small measurable cardinals

Yair Hayut, Asaf Karagila

We continue the work from [8] and make a small -- but significant -- improvement to the definition of $j$ -decomposable system. This provides us with a better lifting of elementary…

math.LO2022★ 1 cited

The Gluing Property

Yair Hayut, Alejandro Poveda

We introduce a new compactness principle which we call the gluing property. For a measurable cardinal $κ$ and a cardinal $λ$ , we say that $κ$ has the $λ$ -gluing property if every s…

math.LO2021★ 1 cited

The Variety of Projection of a Tree-Prikry Forcing

Tom Benhamou, Moti Gitik, Yair Hayut

We study which $κ$ -distributive forcing notions of size $κ$ can be embedded into tree Prikry forcing notions with $κ$ -complete ultrafilters under various large cardinal assumptions…

math.LO2021★ 1 cited

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.

math.DG2021

Complete $S E (3)$ invariants for a comeagre set of $C^{3}$ compact orientable surfaces in $R^{3}$

Yair Hayut, David Lehavi

We introduce invariants for compact $C^{1}$ -orientable surfaces (with boundary) in $R^{3}$ up to rigid transformations. Our invariants are certain degree four polynomials in t…

math.LO2020

Subcompact cardinals, type omission and ladder systems

Yair Hayut, Menachem Magidor

We provide a model theoretical and tree property like characterization of $λ$ - $Π_{1}^{1}$ -subcompactness and supercompactness. We explore the behaviour of those combinatorial principle…

math.LO2019

On $ω$ -Strongly Measurable Cardinals

Omer Ben-Neria, Yair Hayut

We prove several consistency results concerning the notion of $ω$ -strongly measurable cardinal in HOD. In particular, we show that is it consistent, relative to a large cardinal hy…

math.LO2019

A note on the normal filters extension property

Yair Hayut

We show that if $λ^{< κ} = λ$ and every normal filter on $P_{κ} λ$ can be extended to a $κ$ -complete ultrafilter then so does every $κ$ -complete filter on $λ$ . This answers a question…

math.LO2019

Perfect Subtree Property for Weakly Compact Cardinals

Yair Hayut, Sandra Müller

We investigate the consistency strength of the statement: $κ$ is weakly compact and there is no tree on $κ$ with exactly $κ^{+}$ many branches. We show that this statement fails st…

math.LO2019

Dowker filters and Magidor forcing

Shimon Garti, Yair Hayut

We prove that the consistency of the existence of a Dowker filter at $κ^{+}$ along with $2^{κ} = κ^{+}$ where $κ$ is regular and uncountable. Using Magidor forcing we also prove the consis…

math.LO2019

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 $ν$ such that the singular cardinal hypothesis fails at $ν$ and eve…

math.LO2019

Identity crises between supercompactness and Vopenka's Principle

Yair Hayut, Menachem Magidor, Alejandro Poveda

In this paper we study the notion of $C^{(n)}$ -supercompactness introduced by Bagaria in \cite{Bag} and prove the identity crises phenomenon for such class. Specifically, we show t…

Compactness phenomena in HOD and the Optimality of Magidor's Covering theorem

More notions of forcing add a square

The directedness of the Rudin-Keisler order at measurable cardinals

The tree property on long intervals of regular cardinals

Isomorphism Classes of Generating Sets

On a problem of Erdos and Hajnal

Dense ideals

Intermediate models with deep failure of choice

The first measurable can be the first inaccessible cardinal

Sealed Kurepa Trees

Prikry type forcings and the Bukovský-Dehornoy phenomena

The Spectra of transitive models

Small measurable cardinals

The Gluing Property

The Variety of Projection of a Tree-Prikry Forcing

Mutually embeddable models of ZFC

Complete SE(3) invariants for a comeagre set of C3 compact orientable surfaces in R3

Subcompact cardinals, type omission and ladder systems

On ω-Strongly Measurable Cardinals

A note on the normal filters extension property

Perfect Subtree Property for Weakly Compact Cardinals

Dowker filters and Magidor forcing

Stationary Reflection and the failure of SCH

Identity crises between supercompactness and Vopenka's Principle

Complete $S E (3)$ invariants for a comeagre set of $C^{3}$ compact orientable surfaces in $R^{3}$

On $ω$ -Strongly Measurable Cardinals