Set theory beyond the first uncountable cardinal

Project Information

BeyondA1

Grant agreement ID: 802756

DOI

10.3030/802756

Project closed

EC signature date 12 September 2018

Start date 1 October 2018

End date 30 September 2024

Funded under

• EXCELLENT SCIENCE - European Research Council (ERC)

Total cost

€ 1 362 500,00

EU contribution

€ 1 362 500,00

Coordinated by

BAR ILAN UNIVERSITY
Israel

CORDIS provides links to public deliverables and publications of HORIZON projects.

Links to deliverables and publications from FP7 projects, as well as links to some specific result types such as dataset and software, are dynamically retrieved from OpenAIRE .

Publications

Peer reviewed articles (42)

ON THE COFINALITY OF THE LEAST -STRONGLY COMPACT CARDINAL

Author(s): ZHIXING YOU, JIACHEN YUAN
Published in: The Journal of Symbolic Logic, Issue 89, 2024, Page(s) 569-582, ISSN 0022-4812
Publisher: Association for Symbolic Logic
DOI: 10.1017/jsl.2023.4

A CLUB GUESSING TOOLBOX I

Author(s): TANMAY INAMDAR, ASSAF RINOT
Published in: The Bulletin of Symbolic Logic, Issue 30, 2025, Page(s) 303-361, ISSN 1079-8986
Publisher: Association for Symbolic Logic
DOI: 10.1017/bsl.2024.27

Approachable free subsets and fine structure derived scales

Author(s): Dominik Adolf, Omer Ben-Neria
Published in: Annals of Pure and Applied Logic, Issue 175, 2024, Page(s) 103428, ISSN 0168-0072
Publisher: Elsevier BV
DOI: 10.1016/j.apal.2024.103428

DIAMOND ON LADDER SYSTEMS AND COUNTABLY METACOMPACT TOPOLOGICAL SPACES

Author(s): RODRIGO CARVALHO, TANMAY INAMDAR, ASSAF RINOT
Published in: The Journal of Symbolic Logic, 2024, Page(s) 1-20, ISSN 0022-4812
Publisher: Association for Symbolic Logic
DOI: 10.1017/jsl.2024.40

What would the rational Urysohn space and the random graph look like if they were uncountable?

Author(s): Ziemowit Kostana
Published in: Archive for Mathematical Logic, 2024, ISSN 0933-5846
Publisher: Springer Verlag
DOI: 10.1007/s00153-024-00948-z

COFINAL TYPES BELOW

Author(s): ROY SHALEV
Published in: The Journal of Symbolic Logic, 2023, Page(s) 1-26, ISSN 0022-4812
Publisher: Association for Symbolic Logic
DOI: 10.1017/jsl.2023.32

Was Ulam right? I: Basic theory and subnormal ideals

Author(s): Inamdar, Tanmay; Rinot, Assaf
Published in: Topology and its applications, Issue 323(C), 2023, Page(s) 108287, ISSN 0166-8641
Publisher: Elsevier BV
DOI: 10.1016/j.topol.2022.108287

A guessing principle from a Souslin tree, with applications to topology

Author(s): Assaf Rinot; Roy Shalev
Published in: Topology and its applications, Issue 323(C), 2023, Page(s) 108296, ISSN 0166-8641
Publisher: Elsevier BV
DOI: 10.48550/arxiv.2104.09150

Ramsey theory over partitions II: Negative Ramsey relations and pump-up theorems

Author(s): Menachem Kojman, Assaf Rinot, Juris Steprāns
Published in: Israel Journal of Mathematics, Issue 261, 2024, Page(s) 223-247, ISSN 0021-2172
Publisher: Magnes Press
DOI: 10.1007/s11856-023-2574-9

Knaster and friends III: Subadditive colorings

Author(s): Chris Lambie-Hanson, Assaf Rinot
Published in: Journal of Symbolic Logic, 2023, ISSN 0022-4812
Publisher: Association for Symbolic Logic
DOI: 10.1017/jsl.2022.50

Full Souslin trees at small cardinals

Author(s): Assaf Rinot, Shira Yadai, Zhixing You
Published in: Journal of the London Mathematical Society, Issue 110, 2024, ISSN 0024-6107
Publisher: Oxford University Press
DOI: 10.1112/jlms.12957

Was Ulam right? II: small width and general ideals

Author(s): Tanmay Inamdar, Assaf Rinot
Published in: Algebra universalis, Issue 85, 2024, ISSN 0002-5240
Publisher: Birkhauser Verlag
DOI: 10.1007/s00012-024-00843-x

Absoluteness for the theory of the inner model constructed from finitely many cofinality quantifiers

Author(s): Ur Ya'ar
Published in: Annals of Pure and Applied Logic, Issue 175, 2024, Page(s) 103358, ISSN 0168-0072
Publisher: Elsevier BV
DOI: 10.1016/j.apal.2023.103358

On the ideal J[κ]

Author(s): Assaf Rinot
Published in: Annals of Pure and Applied Logic, Issue 173/2, 2022, Page(s) 103055, ISSN 0168-0072
Publisher: Elsevier BV
DOI: 10.1016/j.apal.2021.103055

Sigma-Prikry forcing III: Down to Aleph_omega

Author(s): Poveda, Alejandro; Rinot, Assaf; Sinapova, Dima
Published in: Advances in Mathematics, Issue 1, 2023, Page(s) 109377, ISSN 0001-8708
Publisher: Academic Press
DOI: 10.48550/arxiv.2209.10501

The isomorphism relation of theories with S-DOP in the generalised Baire spaces

Author(s): Miguel Moreno
Published in: Annals of Pure and Applied Logic, Issue 173/2, 2022, Page(s) 103044, ISSN 0168-0072
Publisher: Elsevier BV
DOI: 10.1016/j.apal.2021.103044

Tall Cardinals in Extender Models

Author(s): Gabriel Fernandes; Ralf Schindler
Published in: Notre Dame Journal of Formal Logic, Issue 62/3, 2021, Page(s) 425--454, ISSN 0029-4527
Publisher: University of Notre Dame
DOI: 10.1215/00294527-2021-0023

A new small Dowker space

Author(s): Assaf Rinot, Roy Shalev, Stevo Todorcevic
Published in: Periodica Mathematica Hungarica, Issue 88, 2024, Page(s) 102-117, ISSN 0031-5303
Publisher: Akademiai Kiado
DOI: 10.1007/s10998-023-00541-6

Knaster and friends II: The C-sequence number

Author(s): Chris Lambie-Hanson, Assaf Rinot
Published in: Journal of Mathematical Logic, Issue 21/01, 2021, Page(s) 2150002, ISSN 0219-0613
Publisher: Singapore University Press
DOI: 10.1142/s0219061321500021

Ramsey theory over partitions III: Strongly Luzin sets and partition relations

Author(s): Menachem Kojman; Assaf Rinot; Juris Steprāns.
Published in: Proceedings of the American Mathematical Society, Issue 151/1, 2023, Page(s) 369--384, ISSN 0002-9939
Publisher: American Mathematical Society
DOI: 10.1090/proc/16106

Approximating diamond principles on products at an inaccessible cardinal

Author(s): Omer Ben-Neria, Jing Zhang
Published in: Transactions of the American Mathematical Society, Issue 376, 2023, Page(s) 5923-5948, ISSN 0002-9947
Publisher: American Mathematical Society
DOI: 10.1090/tran/8945

Ramsey theory over partitions I: Positive Ramsey relations from forcing axioms

Author(s): Menachem Kojman, Assaf Rinot, Juris Steprāns
Published in: Israel Journal of Mathematics, Issue 261, 2024, Page(s) 205-222, ISSN 0021-2172
Publisher: Magnes Press
DOI: 10.1007/s11856-023-2573-x

Sums of triples in Abelian groups

Author(s): Ido Feldman, Assaf Rinot
Published in: Mathematika, Issue 69/3, 2023, Page(s) 622--664, ISSN 0025-5793
Publisher: University College London, Department of Mathematics
DOI: 10.1112/mtk.12200

More minimal non-$$\sigma $$-scattered linear orders

Author(s): Roy Shalev
Published in: European Journal of Mathematics, Issue 10, 2024, Page(s) 21, ISSN 2199-675X
Publisher: European Journal of Mathematics
DOI: 10.1007/s40879-024-00780-y

Transformations of the transfinite plane

Author(s): Assaf Rinot, Jing Zhang
Published in: Forum of Mathematics, Sigma, Issue 9, 2021, ISSN 2050-5094
Publisher: Cambridge University Press
DOI: 10.1017/fms.2021.14

A Remark on Schimmerling’s Question

Author(s): Ari Meir Brodsky, Assaf Rinot
Published in: Order, Issue 36/3, 2019, Page(s) 525-561, ISSN 0167-8094
Publisher: Kluwer Academic Publishers
DOI: 10.1007/s11083-019-09482-7

Souslin trees at successors of regular cardinals

Author(s): Assaf Rinot
Published in: Mathematical Logic Quarterly, Issue 65/2, 2019, Page(s) 200-204, ISSN 0942-5616
Publisher: John Wiley & Sons Ltd.
DOI: 10.1002/malq.201800065

Partitioning a reflecting stationary set

Author(s): Maxwell Levine, Assaf Rinot
Published in: Proceedings of the American Mathematical Society, 2020, Page(s) 1, ISSN 0002-9939
Publisher: American Mathematical Society
DOI: 10.1090/proc/14783

On ${\Sigma }_1^1$-completeness of quasi-orders on $\kappa ^\kappa $

Author(s): Tapani Hyttinen, Vadim Kulikov, Miguel Moreno
Published in: Fundamenta Mathematicae, 2020, ISSN 0016-2736
Publisher: Polska Akademia Nauk
DOI: 10.4064/fm679-1-2020

Sigma-Prikry forcing I: The Axioms

Author(s): Alejandro Poveda, Assaf Rinot, Dima Sinapova
Published in: Canadian Journal of Mathematics, 2020, Page(s) 1-38, ISSN 0008-414X
Publisher: Canadian Mathematical Society
DOI: 10.4153/s0008414x20000425

ON UNSUPERSTABLE THEORIES IN GDST

Author(s): MIGUEL MORENO
Published in: The Journal of Symbolic Logic, 2023, Page(s) 1-27, ISSN 0022-4812
Publisher: Association for Symbolic Logic
DOI: 10.1017/jsl.2023.82

More Ramsey theory for highly connected monochromatic subgraphs

Author(s): Michael Hrušák, Saharon Shelah, Jing Zhang
Published in: Canadian Journal of Mathematics, 2024, Page(s) 1-15, ISSN 0008-414X
Publisher: Canadian Mathematical Society
DOI: 10.4153/s0008414x23000767

Fake reflection

Author(s): Gabriel Fernandes; Miguel Moreno; Assaf Rinot
Published in: Israel Journal of Mathematics, Issue 245/1, 2021, Page(s) 295--345, ISSN 0021-2172
Publisher: Magnes Press
DOI: 10.48550/arxiv.2003.08340

Complicated colorings, revisited

Author(s): Assaf Rinot; Jing Zhang
Published in: Annals of Pure and Applied Logic, Issue 174/4, 2023, Page(s) 103243, ISSN 0168-0072
Publisher: Elsevier BV
DOI: 10.1016/j.apal.2022.103243

A Shelah group in ZFC

Author(s): Poór, Márk; Rinot, Assaf
Published in: Forum of Mathematics. Pi, Issue 2, 2025, Page(s) 29, ISSN 2050-5086
Publisher: Cambridge University Press
DOI: 10.1017/fmp.2025.5

How far is almost strong compactness from strong compactness

Author(s): Zhixing You, Jiachen Yuan
Published in: Journal of Mathematical Logic, 2023, ISSN 0219-0613
Publisher: Singapore University Press
DOI: 10.1142/s0219061324500090

Lower consistency bounds for mutual stationarity with divergent cofinalities and limited covering

Author(s): Adolf, Dominik
Published in: Israel Journal of Mathematics, 2023, ISSN 0021-2172
Publisher: Magnes Press
DOI: 10.1007/s11856-022-2401-8

Sigma-Prikry forcing II: Iteration Scheme

Author(s): Alejandro Poveda, Assaf Rinot, Dima Sinapova.
Published in: Journal of Mathematical Logic, Issue 22/3, 2022, Page(s) 2150019, ISSN 0219-0613
Publisher: Singapore University Press
DOI: 10.1142/s0219061321500197

A microscopic approach to Souslin-tree construction, Part II

Author(s): Ari Meir Brodsky, Assaf Rinot
Published in: Annals of Pure and Applied Logic, Issue 172/5, 2021, Page(s) 102904, ISSN 0168-0072
Publisher: Elsevier BV
DOI: 10.1016/j.apal.2020.102904

Partitions of topological spaces and a new club-like principle

Author(s): Rodrigo Carvalho, Gabriel Fernandes, Lúcia R. Junqueira
Published in: Proceedings of the American Mathematical Society, Issue 151, 2023, Page(s) 1787--1800, ISSN 0002-9939
Publisher: American Mathematical Society
DOI: 10.1090/proc/16208

Inclusion modulo nonstationary

Author(s): Gabriel Fernandes, Miguel Moreno, Assaf Rinot
Published in: Monatshefte für Mathematik, Issue 192/4, 2020, Page(s) 827-851, ISSN 0026-9255
Publisher: Springer Verlag
DOI: 10.1007/s00605-020-01431-6

Strongest Transformations

Author(s): Assaf Rinot, Jing Zhang
Published in: Combinatorica, 2023, ISSN 0209-9683
Publisher: Springer Verlag
DOI: 10.1007/s00493-023-00011-0