Research
Notes
Projects

Indestructibility for Ramsey and Ramseylike cardinals
V. Gitman and T. A. Johnstone, “Indestructibility for Ramsey and Ramseylike cardinals,” Manuscript.
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Publications

Model theoretic characterizations of large cardinals revisited
W. Boney, S. Dimopoulos, V. Gitman, and M. Magidor, “Model theoretic characterizations of large cardinals revisited,” Manuscript.
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The virtual large cardinal hierarchy
V. Gitman, S. Dimopoulos, and D. S. Nielsen, “The virtual large cardinal hierarchy,” Manuscript.
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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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KelleyMorse set theory does not prove the class Fodor principle
V. Gitman, J. D. Hamkins, and A. Karagila, “KelleyMorse set theory does not prove the class Fodor theorem,” To appear in Fundamenta Mathematicae.
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Forcing a $\square(\kappa)$like principle to hold at a weakly compact cardinal
B. Cody, V. Gitman, and C. LambieHanson, “A $\square(κ)$like principle consistent with weak compactntess,” To appear in the Annals of Pure and Applied Logic.
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Booleanvalued class forcing
C. Antos, S. D. Friedman, and V. Gitman, “Booleanvalued class forcing,” Manuscript.
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A model of secondorder arithmetic satisfying AC but not DC
S.D. Friedman, V. Gitman, and V. Kanovei, “A model of secondorder arithmetic satisfying AC but not DC,” J. Math. Log., vol. 19, no. 1, pp. 1850013, 39, 2019. Available at: https://doi.org/10.1142/S0219061318500137
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The exact strength of the class forcing theorem
V. Gitman, J. D. Hamkins, P. Holy, P. Schlicht, and K. Williams, “The exact strength of the class forcing theorem,” To appear in the Journal of Symbolic Logic.
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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. 12, pp. 245–265, 2019. Available at: https://doi.org/10.1007/s0015301806325
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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. Available at: https://doi.org/10.1016/j.apal.2018.08.005
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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. 12, pp. 1–20, 2017. Available at: http://dx.doi.org/10.1007/s001530160511x
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Mitchell order for Ramsey and Ramseylike cardinals
E. Carmody, V. Gitman, and M. E. Habič, “A Mitchelllike order for Ramsey and Ramseylike cardinals,” Fund. Math., vol. 248, no. 1, pp. 1–32, 2020. Available at: https://doi.org/10.4064/fm70132019
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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. Available at: https://doi.org/10.1090/conm/690
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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. Available at: https://doi.org/10.1215/0029452720180007
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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. 78, pp. 961–984, 2015. Available at: http://dx.doi.org/10.1007/s0015301504538
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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. 12, pp. 66–76, 2017. Available at: https://doi.org/10.1002/malq.201500002
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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. 45, pp. 391–406, 2016. Available at: http://dx.doi.org/10.1002/malq.201500019
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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. Available at: http://dx.doi.org/10.1215/002945272010030
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Ramseylike cardinals II
V. Gitman and P. D. Welch, “Ramseylike cardinals II,” The Journal of Symbolic Logic, vol. 76, no. 2, pp. 541–560, 2011. Available at: http://dx.doi.org/10.2178/jsl/1305810763
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Ramseylike cardinals
V. Gitman and P. D. Welch, “Ramseylike cardinals II,” The Journal of Symbolic Logic, vol. 76, no. 2, pp. 541–560, 2011. Available at: http://dx.doi.org/10.2178/jsl/1305810763
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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. Available at: http://dx.doi.org/10.1002/malq.200810015
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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. Available at: https://doi.org/10.2178/jsl/1230396751
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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. Available at: http://gateway.proquest.com/openurl?url_ver=Z39.882004&rft_val_fmt=info:ofi/fmt:kev:mtx:dissertation&res_dat=xri:pqdiss&rft_dat=xri:pqdiss:3283199
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