Research
Notes
Projects

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


Structural properties of the stable core
S.D. Friedman, V. Gitman, and S. Müller, “Some properties of the Stable Core,” Manuscript.
PDF Bibtex 
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,” Submitted.
PDF Bibtex 
A $\square(\kappa)$like principle consistent with weak compactness
B. Cody, V. Gitman, and C. LambieHanson, “A $\square(κ)$like principle consistent with weak compactness,” Submitted.
PDF Bibtex 
Booleanvalued class forcing
C. Antos, S. D. Friedman, and V. Gitman, “Booleanvalued class forcing,” Submitted.
PDF Bibtex 
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://victoriagitman.github.io/files/ModelOfACNotDC.pdf
PDF Bibtex 
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.
PDF Bibtex Arχiv 
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.
PDF Bibtex Arχiv 
Virtual large cardinals
V. Gitman and R. Schindler, “Virtual large cardinals,” Ann. Pure Appl. Logic, vol. 169, no. 12, pp. 1317–1334, 2018.
PDF Bibtex 
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
PDF Bibtex 
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.
PDF Bibtex 
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.
PDF Bibtex Arχiv 
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
PDF Bibtex Arχiv 
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
PDF Bibtex Arχiv 
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
PDF Bibtex Arχiv 
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.
PDF Bibtex Arχiv 
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.
PDF Bibtex Arχiv 
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
PDF Bibtex Arχiv 
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.
PDF Bibtex Arχiv 
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
PDF Bibtex Arχiv 
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
PDF Bibtex Arχiv 
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
PDF Bibtex Arχiv 
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
PDF Bibtex Arχiv 
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
PDF Bibtex Arχiv 
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
PDF Bibtex