Research
Notes
Publications
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Parameter-free schemes in second-order arithmetic V. Gitman, “Parameter-free schemes in second-order arithmetic,” Manuscript.
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Upward Löwenheim-Skolem numbers for abstract logics V. Gitman and J. Osinski, “Upward Löwenheim-Skolem numbers for abstract logics,” Manuscript, 2023.
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Between Ramsey and measurable cardinals V. Gitman and P. Schlicht, “Between Ramsey and measurable cardinals,” Manuscript, 2023.
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Jensen forcing at an inaccessible and a model of Kelley-Morse satisfying ${\rm CC}$ but not ${\rm DC}_\omega$ S.-D. Friedman and V. Gitman, “Jensen forcing at an inaccessible and a model of Kelley-Morse satisfying ${\rm CC}$ but not ${\rm DC}_ω$,” Manuscript, 2023.
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ZFC without Power Set II: Reflection Strikes Back V. Gitman and R. Matthews, “ZFC without Power Set II: Reflection Strikes Back,” To appear in Fundamenta Mathematicae, 2022.
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Indestructibility for Ramsey and Ramsey-like cardinals V. Gitman and T. A. Johnstone, “Indestructibility properties of Ramsey and Ramsey-like cardinals,” Ann. Pure Appl. Logic, vol. 173, no. 6, pp. Paper No. 103106, 30, 2022.
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Model theoretic characterizations of large cardinals revisited W. Boney, S. Dimopoulos, V. Gitman, and M. Magidor, “Model theoretic characterizations of large cardinals revisited,” To appear in the Transactions of the AMS.
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The virtual large cardinal hierarchy V. Gitman, S. Dimopoulos, and D. S. Nielsen, “The virtual large cardinal hierarchy,” To appear in Fundamenta Mathematicae.
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Modern class forcing C. Antos and V. Gitman, “Modern Class Forcing,” in Research Trends in Contemporary Logic, College Publications, Forthcoming.
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Structural properties of the stable core S.-D. Friedman, V. Gitman, and S. Müller, “Some properties of the Stable Core,” Manuscript.
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Kelley-Morse set theory does not prove the class Fodor principle V. Gitman, J. D. Hamkins, and A. Karagila, “Kelley-Morse set theory does not prove the class Fodor principle,” Fund. Math., vol. 254, no. 2, pp. 133–154, 2021.
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Forcing a $\square(\kappa)$-like principle to hold at a weakly compact cardinal B. Cody, V. Gitman, and C. Lambie-Hanson, “A $\square(κ)$-like principle consistent with weak compactntess,” To appear in the Annals of Pure and Applied Logic.
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Boolean-valued class forcing C. Antos, S.-D. Friedman, and V. Gitman, “Boolean-valued class forcing,” Fund. Math., vol. 255, no. 3, pp. 231–254, 2021.
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A model of second-order arithmetic satisfying AC but not DC S.-D. Friedman, V. Gitman, and V. Kanovei, “A model of second-order arithmetic satisfying AC but not DC,” J. Math. Log., vol. 19, no. 1, pp. 1850013, 39, 2019.
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The exact strength of the class forcing theorem V. Gitman, J. D. Hamkins, P. Holy, P. Schlicht, and K. J. Williams, “The exact strength of the class forcing theorem,” J. Symb. Log., vol. 85, no. 3, pp. 869–905, 2020. Available at: https://doi.org/10.1017/jsl.2019.89
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A model of the generic Vopěnka principle in which the ordinals are not Mahlo V. Gitman and J. D. Hamkins, “A model of the generic Vopěnka principle in which the ordinals are not Mahlo,” Arch. Math. Logic, vol. 58, no. 1-2, pp. 245–265, 2019.
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Virtual large cardinals V. Gitman and R. Schindler, “Virtual large cardinals,” Ann. Pure Appl. Logic, vol. 169, no. 12, pp. 1317–1334, 2018.
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Generic Vopěnka's Principle, remarkable cardinals, and the weak Proper Forcing Axiom J. Bagaria, V. Gitman, and R. Schindler, “Generic Vopěnka’s Principle, remarkable cardinals, and the weak Proper Forcing Axiom,” Arch. Math. Logic, vol. 56, no. 1-2, pp. 1–20, 2017.
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Mitchell order for Ramsey and Ramsey-like cardinals E. Carmody, V. Gitman, and M. E. Habič, “A Mitchell-like order for Ramsey and Ramsey-like cardinals,” Fund. Math., vol. 248, no. 1, pp. 1–32, 2020.
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Open determinacy for class games V. Gitman and J. D. Hamkins, “Open determinacy for class games,” in Foundations of mathematics, vol. 690, Amer. Math. Soc., Providence, RI, 2017, pp. 121–143.
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Ehrenfeucht's lemma in set theory G. Fuchs, V. Gitman, and J. D. Hamkins, “Ehrenfeucht’s lemma in set theory,” Notre Dame J. Form. Log., vol. 59, no. 3, pp. 355–370, 2018.
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Indestructibility properties of remarkable cardinals Y. Cheng and V. Gitman, “Indestructibility properties of remarkable cardinals,” Arch. Math. Logic, vol. 54, no. 7-8, pp. 961–984, 2015.
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Incomparable $\omega_1$-like models of set theory G. Fuchs, V. Gitman, and J. D. Hamkins, “Incomparable $\omega_1$-like models of set theory,” MLQ Math. Log. Q., vol. 63, no. 1-2, pp. 66–76, 2017.
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On ground model definability V. Gitman and T. A. Johnstone, “On ground model definability,” in Infinity, Computability, and Metamathematics: Festschrift in honour of the 60th birthdays of Peter Koepke and Philip Welch, London, GB: College publications, 2014.
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Easton's theorem for Ramsey and strongly Ramsey cardinals V. Gitman and B. Cody, “Easton’s theorem for Ramsey and strongly Ramsey cardinals,” Annals of Pure and Applied Logic, vol. 166, no. 9, pp. 934–952, 2015.
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What is the theory ZFC without power set? V. Gitman, J. D. Hamkins, and T. A. Johnstone, “What is the theory $\mathsf {ZFC}$ without power set?,” MLQ Math. Log. Q., vol. 62, no. 4-5, pp. 391–406, 2016.
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Inner models with large cardinal features usually obtained by forcing A. Apter, V. Gitman, and J. D. Hamkins, “Inner models with large cardinal features usually obtained by forcing,” Archive for Mathematical Logic, vol. 51, no. 3, pp. 257–283, 2012.
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A natural model of the multiverse axioms V. Gitman and J. D. Hamkins, “A natural model of the multiverse axioms,” Notre Dame J. Form. Log., vol. 51, no. 4, pp. 475–484, 2010.
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Ramsey-like cardinals II V. Gitman and P. D. Welch, “Ramsey-like cardinals II,” The Journal of Symbolic Logic, vol. 76, no. 2, pp. 541–560, 2011.
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Ramsey-like cardinals V. Gitman and P. D. Welch, “Ramsey-like cardinals II,” The Journal of Symbolic Logic, vol. 76, no. 2, pp. 541–560, 2011.
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Proper and piecewise proper families of reals V. Gitman, “Proper and Piecewise Proper Families of Reals,” Mathematical Logic Quarterly, vol. 55, no. 5, pp. 542–550, 2009.
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Scott’s problem for proper Scott sets V. Gitman, “Scott’s problem for proper Scott sets,” J. Symbolic Logic, vol. 73, no. 3, pp. 845–860, 2008.
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Applications of the proper forcing axiom to models of Peano Arithmetic V. Gitman, Applications of the proper forcing axiom to models of Peano arithmetic. ProQuest LLC, Ann Arbor, MI, 2007, p. 149.
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