publications

Papers, preprints, and books

2026

  1. Ultrapowers of determinacy models as iteration trees on HOD
    Gabriel Goldberg, Grigor Sargsyan, and Benjamin Siskind
    Preprint, 2026.
    arXiv
  2. The failure of square at all uncountable cardinals is weaker than a Woodin limit of Woodin cardinals
    Douglas Blue, Paul Larson, and Grigor Sargsyan
    Preprint, 2026.
    arXiv
  3. Hjorth’s reflection argument
    Grigor Sargsyan
    Forum of Mathematics, Sigma 14, e2 (2026).
    arXiv DOI
  4. Determinacy in the Chang model
    Takehiko Gappo, and Grigor Sargsyan
    Proceedings of the American Mathematical Society 154(4), 1763–1769 (2026).
    arXiv DOI
  5. Unreachability of inductive-like pointclasses in \(L(\mathbb{R})\)
    Derek Levinson, Itay Neeman, and Grigor Sargsyan
    The Journal of Symbolic Logic 91(1), 175–209 (2026).
    arXiv DOI

2025

  1. Partial Tower Sealing
    Grigor Sargsyan, and Nam Trang
    Preprint, 2025.
    arXiv
  2. A model of the Axiom of Determinacy in which every set of reals is universally Baire
    Paul B. Larson, Grigor Sargsyan, and Trevor Wilson
    Forum of Mathematics, Sigma 13, e94 (2025).
    arXiv DOI
  3. Erratum: On \(\omega\)-strongly measurable cardinals in \(\mathbb{P}_{\max}\) extensions
    Navin Aksornthong, Takehiko Gappo, James Holland, and Grigor Sargsyan
    Journal of Mathematical Logic 25(3), 2492001 (2025).
    DOI
  4. Nairian Models
    Douglas Blue, Paul B. Larson, and Grigor Sargsyan
    Preprint, 2025.
    arXiv
  5. Gödel’s Program in Set Theory
    Sandra Müller, and Grigor Sargsyan
    Monatshefte für Mathematik 208(4), 729–750 (2025).
    arXiv DOI
  6. \(\mathsf{AD}^{+}\) implies \(\omega_1\) is a club \(\Theta\)-Berkeley cardinal
    Douglas Blue, and Grigor Sargsyan
    Forum of Mathematics, Sigma 13, e126 (2025).
    arXiv DOI
  7. Chang models over derived models with supercompact measures
    Takehiko Gappo, Sandra Müller, and Grigor Sargsyan
    Journal of Mathematical Logic 25(2), 2550007 (2025).
    arXiv DOI
  8. On \(\omega\)-strongly measurable cardinals in \(\mathbb{P}_{\max}\) extensions
    Navin Aksornthong, Takehiko Gappo, James Holland, and Grigor Sargsyan
    Journal of Mathematical Logic 25(2), 2450018 (2025).
    arXiv DOI
  9. Towards a generic absoluteness theorem for Chang models
    Sandra Müller, and Grigor Sargsyan
    Advances in Mathematics 476, 110357 (2025).
    arXiv DOI

2024

  1. Building Models of Determinacy from Below
    Obrad Kasum, and Grigor Sargsyan
    Preprint, 2024.
    arXiv
  2. Ideals and Strong Axioms of Determinacy
    Dominik Adolf, Grigor Sargsyan, Nam Trang, Trevor M. Wilson, and Martin Zeman
    Journal of the American Mathematical Society 37(4), 1203–1273 (2024).
    arXiv DOI
  3. The Largest Suslin Axiom
    Grigor Sargsyan, and Nam Trang
    Lecture Notes in Logic 56. Cambridge University Press (2024).
    arXiv DOI
  4. The exact consistency strength of the generic absoluteness for the universally Baire sets
    Grigor Sargsyan, and Nam Trang
    Forum of Mathematics, Sigma 12, e12 (2024).
    arXiv DOI Corrigendum
  5. Forcing more DC over the Chang model using the Thorn sequence
    James Holland, and Grigor Sargsyan
    Proceedings of the American Mathematical Society 152(7), 3111–3122 (2024).
    arXiv DOI

2023

  1. Generic Generators
    Grigor Sargsyan
    Preprint, 2023.
    arXiv
  2. Negative results on precipitous ideals on \(\omega_1\)
    Grigor Sargsyan
    J. Symb. Log. 88(2), 490–509 (2023).
    arXiv DOI

2022

  1. Suslin cardinals and cutpoints in mouse limits
    Stephan Jackson, Grigor Sargsyan, and John Steel
    Preprint, 2022.
    arXiv
  2. On the derived models of self-iterable universes
    Takehiko Gappo, and Grigor Sargsyan
    Proc. Am. Math. Soc. 150(3), 1321–1329 (2022).
    arXiv DOI

2021

  1. A characterization of extenders of HOD
    Grigor Sargsyan
    Preprint, 2021.
    arXiv
  2. Varsovian models II
    Grigor Sargsyan, Ralf Schindler, and Farmer Schlutzenberg
    Preprint, 2021.
    arXiv
  3. Failures of square in Pmax extensions of Chang models
    Paul B. Larson, and Grigor Sargsyan
    Preprint, 2021.
    arXiv
  4. Sealing of the universally Baire sets
    Grigor Sargsyan, and Nam Trang
    Bull. Symb. Log. 27(3), 254–266 (2021).
    DOI Website
  5. HOD in inner models with Woodin cardinals
    Sandra Müller, and Grigor Sargsyan
    J. Symb. Log. 86(3), 871–896 (2021).
    arXiv DOI
  6. Covering with Chang models over derived models
    Grigor Sargsyan
    Adv. Math. 384, 21 (2021).
    Id/No 107717
    arXiv DOI
  7. Sealing from iterability
    Grigor Sargsyan, and Nam Trang
    Trans. Am. Math. Soc., Ser. B 8, 229–248 (2021).
    arXiv DOI
  8. \(\mathsf{AD}_{\mathbb{R}}\) implies that all sets of reals are \(\Theta\) universally Baire
    Grigor Sargsyan
    Arch. Math. Logic 60(1-2), 1–15 (2021).
    arXiv DOI

2020

  1. Trends in set theory. Simon Fest conference in honor of Simon Thomas’s 60th birthday, Rutgers University, Piscataway, New Jersey, USA, September 15–17, 2017
    Contemp. Math. 752. Providence, RI: American Mathematical Society (AMS) (2020).
    DOI

2019

  1. An inner model theoretic proof of Becker’s theorem
    Grigor Sargsyan
    Arch. Math. Logic 58(7-8), 999–1003 (2019).
    arXiv DOI
  2. Derived models of mice below the least fixpoint of the Solovay sequence
    Dominik Adolf, and Grigor Sargsyan
    J. Symb. Log. 84(1), 27–53 (2019).
    DOI Website
  3. HOD up to \(\mathsf{AD}_{\mathbb{R}}+\text{“}\Theta\text{ is measurable”}\)
    Rachid Atmai, and Grigor Sargsyan
    Ann. Pure Appl. Logic 170(1), 95–108 (2019).
    arXiv DOI

2018

  1. Varsovian models. I
    Grigor Sargsyan, and Ralf Schindler
    J. Symb. Log. 83(2), 496–528 (2018).
    DOI Website

2017

  1. Translation procedures in descriptive inner model theory
    Grigor Sargsyan
    In Foundations of mathematics. Logic at Harvard. Essays in honor of W. Hugh Woodin’s 60th birthday. Proceedings of the Logic at Harvard conference, Harvard University, Cambridge, MA, USA, March 27–29, 2015, 205–223 (2017).
    arXiv DOI
  2. Square principles in P_max extensions
    Andrés Eduardo Caicedo, Paul Larson, Grigor Sargsyan, Ralf Schindler, John Steel, and Martin Zeman
    Isr. J. Math. 217, 231–261 (2017).
    arXiv DOI

2016

  1. Tame failures of the unique branch hypothesis and models of \(\mathsf{AD}_{\mathbb{R}}+\text{“}\Theta\text{ is regular”}\)
    Grigor Sargsyan, and Nam Trang
    J. Math. Log. 16(2), 31 (2016).
    Id/No 1650007
    DOI Website

2015

  1. Hod mice and the mouse set conjecture
    Grigor Sargsyan
    Mem. Am. Math. Soc. 236, no. 1111. Providence, RI: American Mathematical Society (AMS) (2015).
    DOI
  2. The mouse set conjecture for sets of reals
    Grigor Sargsyan, and John Steel
    J. Symb. Log. 80(2), 671–683 (2015).
    arXiv DOI
  3. Covering with universally Baire operators
    Grigor Sargsyan
    Adv. Math. 268, 603–665 (2015).
    DOI

2014

  1. An inner model proof of the strong partition property for \(\delta_1^2\)
    Grigor Sargsyan
    Notre Dame J. Formal Logic 55(4), 563–568 (2014).
    arXiv DOI
  2. Nontame mouse from the failure of square at a singular strong limit cardinal
    Grigor Sargsyan
    J. Math. Log. 14(1), 47 (2014).
    Id/No 1450003
    DOI
  3. Non-tame mice from tame failures of the unique branch hypothesis
    Grigor Sargsyan, and Nam Trang
    Can. J. Math. 66(4), 903–923 (2014).
    arXiv DOI

2013

  1. Book review of: Alexander S. Kechris (ed.), Benedikt Löwe (ed.) and John R. Steel (ed.): Wadge degrees and projective ordinals. The Cabal Seminar, Volume II
    Grigor Sargsyan
    Bull. Symb. Log. 19(4), 492–496 (2013).
    DOI
  2. On the prewellorderings associated with the directed systems of mice
    Grigor Sargsyan
    J. Symb. Log. 78(3), 735–763 (2013).
    arXiv DOI
  3. Descriptive inner model theory
    Grigor Sargsyan
    Bull. Symb. Log. 19(1), 1–55 (2013).
    arXiv DOI

2012

  1. Indestructible strong compactness but not supercompactness
    Arthur W. Apter, Moti Gitik, and Grigor Sargsyan
    Ann. Pure Appl. Logic 163(9), 1237–1242 (2012).
    DOI

2010

  1. An equiconsistency for universal indestructibility
    Arthur W. Apter, and Grigor Sargsyan
    J. Symb. Log. 75(1), 314–322 (2010).
    DOI

2009

  1. On the indestructibility aspects of identity crisis
    Grigor Sargsyan
    Arch. Math. Logic 48(6), 493–513 (2009).
    DOI

2008

  1. On HOD-supercompactness
    Grigor Sargsyan
    Arch. Math. Logic 47(7-8), 765–768 (2008).
    DOI
  2. Universal indestructibility for degrees of supercompactness and strongly compact cardinals
    Arthur W. Apter, and Grigor Sargsyan
    Arch. Math. Logic 47(2), 133–142 (2008).
    DOI

2007

  1. A reduction in consistency strength for universal indestructibility
    Arthur W. Apter, and Grigor Sargsyan
    Bull. Pol. Acad. Sci., Math. 55(1), 1–6 (2007).
    DOI

2006

  1. Identity crises and strong compactness. III: Woodin cardinals
    Arthur W. Apter, and Grigor Sargsyan
    Arch. Math. Logic 45(3), 307–322 (2006).
    DOI

2005

  1. Can a large cardinal be forced from a condition implying its negation?
    Arthur W. Apter, and Grigor Sargsyan
    Proc. Am. Math. Soc. 133(10), 3103–3108 (2005).
    DOI

2004

  1. Jonsson-like partition relations and \(j\colon V\to V\)
    Arthur W. Apter, and Grigor Sargsyan
    J. Symb. Log. 69(4), 1267–1281 (2004).
    DOI