Research
Notes
Projects

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

Booleanvalued class forcing
C. Antos, S. D. Friedman, and V. Gitman, “Booleanvalued class forcing,” Submitted.
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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,” To appear in the Journal of Mathematical Logic.
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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,” Submitted.
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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,” To appear in the Archive for Mathematical Logic.
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Virtual large cardinals
V. Gitman and R. Schindler, “Virtual large cardinals,” To appear in the Proceedings of the Logic Colloquium 2015.
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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. Habič, “Mitchell order for Ramsey and Ramseylike cardinals,” To appear in Fundamenta Mathematicae.
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Open determinacy for class games
V. Gitman and J. D. Hamkins, “Open determinacy for class games,” in Foundations of Mathematics, Logic at Harvard, Essays in Honor of Hugh Woodin’s 60th Birthday, A. E. Caicedo, J. Cummings, P. Koellner, and P. Larson, Eds. American Mathematical Society, (expected) 2016. Available at: http://jdh.hamkins.org/opendeterminacyforclassgames
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Ehrenfeucht's lemma in set theory
G. Fuchs, V. Gitman, and J. D. Hamkins, “Ehrenfeucht’s lemma in set theory,” To appear in the Notre Dame Journal of Formal Logic.
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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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