Research

PROJECTS

  • Indestructibility for Ramsey and Ramsey-like cardinals
    • V. Gitman and T. A. Johnstone, “Indestructibility for Ramsey and Ramsey-like cardinals,” Preprint.  
      @ARTICLE{gitman:ramseyindes,
      AUTHOR= {Victoria Gitman and Thomas A. Johnstone},
      TITLE= {Indestructibility for {R}amsey and {R}amsey-like cardinals},
      journal = {Preprint},
      PDF={http://boolesrings.org/victoriagitman/files/2015/09/indestructibleramseycardinalsnew.pdf},
      }

PUBLICATIONS

  • 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)  
      @ARTICLE{GitmanHamkinsHolySchlichtWilliams:ForcingTheorem,
      AUTHOR= {Victoria Gitman and Joel David Hamkins and Peter Holy and Philipp Schlicht and Kameryn Williams},
      TITLE= {The exact strength of the class forcing theorem},
      PDF={https://boolesrings.org/victoriagitman/files/2017/07/Forcing-theorem.pdf},
      Note ={Submitted},
      EPRINT ={1707.03700},
      }

  • A model of the generic Vopěnka principle in which the ordinals are not $\Delta_2$-Mahlo
    • V. Gitman and J. D. Hamkins, “A model of the generic vop\v enka principle in which the ordinals are not $\Delta_2$-mahlo.” (Submitted)  
      @ARTICLE{GitmanHamkins:GVP,
      AUTHOR= {Victoria Gitman and Joel David Hamkins},
      TITLE= {A model of the generic Vop\v enka principle in which the ordinals are not $\Delta_2$-Mahlo},
      PDF={https://boolesrings.org/victoriagitman/files/2017/06/Generic-Vopenka-with-Ord-not-Mahlo.pdf},
      Note ={Submitted},
      EPRINT ={1706.00843},
      }

  • Virtual large cardinals
    • V. Gitman and R. Schindler, “Virtual large cardinals.” (Submitted)  
      @ARTICLE{GitmanSchindler:virtualCardinals,
      AUTHOR= {Gitman, Victoria and Schindler, Ralf},
      TITLE= {Virtual large cardinals},
      Note ={Submitted},
      pdf={https://boolesrings.org/victoriagitman/files/2017/03/virtualLargeCardinals.pdf},
      }

  • Generic Vopěnka’s Principle, remarkable cardinals, and the weak Proper Forcing Axiom
    • J. Bagaria, V. Gitman, and R. Schindler, “Generic Vop\v enka’s Principle, remarkable cardinals, and the weak Proper Forcing Axiom,” Arch. math. logic, vol. 56, iss. 1-2, pp. 1-20, 2017.  
      @ARTICLE{BagariaGitmanSchindler:VopenkaPrinciple,
      AUTHOR = {Bagaria, Joan and Gitman, Victoria and Schindler, Ralf},
      TITLE = {Generic {V}op\v enka's {P}rinciple, remarkable cardinals, and the
      weak {P}roper {F}orcing {A}xiom},
      JOURNAL = {Arch. Math. Logic},
      FJOURNAL = {Archive for Mathematical Logic},
      VOLUME = {56},
      YEAR = {2017},
      NUMBER = {1-2},
      PAGES = {1--20},
      ISSN = {0933-5846},
      MRCLASS = {03E35 (03E55 03E57)},
      MRNUMBER = {3598793},
      DOI = {10.1007/s00153-016-0511-x},
      URL = {http://dx.doi.org/10.1007/s00153-016-0511-x},
      pdf ={http://boolesrings.org/victoriagitman/files/2016/02/GenericVopenkaPrinciples.pdf},
      }

  • Mitchell order for Ramsey and Ramsey-like cardinals
    • E. Carmody, V. Gitman, and M. Habič, “Mitchell order for Ramsey and Ramsey-like cardinals.” (Manuscript under review)  
      @ARTICLE{CarmodyGitmanHabic:MitchellOrder,
      AUTHOR= {Carmody, Erin and Gitman, Victoria and Habi\v{c}, Miha},
      TITLE= {Mitchell order for {R}amsey and {R}amsey-like cardinals},
      Note ={Manuscript under review},
      PDF={http://boolesrings.org/victoriagitman/files/2016/09/MitchellOrderRamseyCardsArxiv.pdf},
      }

  • 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. (Newton Institute preprint ni15064)  
      @INCOLLECTION{GitmanHamkins:OpenDeterminacyForClassGames,
      author = {Victoria Gitman and Joel David Hamkins},
      title = {Open determinacy for class games},
      booktitle = {Foundations of Mathematics, Logic at Harvard, Essays in Honor of Hugh Woodin's 60th Birthday},
      publisher = {American Mathematical Society},
      year = {(expected) 2016},
      editor = {Andr\'es E. Caicedo and James Cummings and Peter Koellner and Paul Larson},
      volume = {},
      number = {},
      series = {Contemporary Mathematics},
      type = {},
      chapter = {},
      pages = {},
      address = {},
      edition = {},
      month = {},
      note = {Newton Institute preprint ni15064},
      url = {http://jdh.hamkins.org/open-determinacy-for-class-games},
      eprint = {1509.01099},
      archivePrefix = {arXiv},
      primaryClass = {math.LO},
      abstract = {},
      keywords = {},
      pdf= {http://boolesrings.org/victoriagitman/files/2016/09/Proper-class-games.pdf},
      }

  • 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.  
      @ARTICLE{fuchsgitmanhamkins:ehrenfeuchtLemma,
      AUTHOR= {Gunter Fuchs and Victoria Gitman and Joel David Hamkins},
      TITLE= {Ehrenfeucht's lemma in set theory},
      PDF={http://boolesrings.org/victoriagitman/files/2015/01/Ehrenfeucht.pdf},
      EPRINT={1501.01918},
      JOURNAL= {To appear in the Notre Dame Journal of Formal Logic}}

  • Indestructibility properties of remarkable cardinals
    • Y. Cheng and V. Gitman, “Indestructibility properties of remarkable cardinals,” Arch. math. logic, vol. 54, iss. 7-8, pp. 961-984, 2015.  
      @ARTICLE{chenggitman:IndestructibleRemarkableCardinals,
      AUTHOR = {Cheng, Yong and Gitman, Victoria},
      TITLE = {Indestructibility properties of remarkable cardinals},
      JOURNAL = {Arch. Math. Logic},
      FJOURNAL = {Archive for Mathematical Logic},
      VOLUME = {54},
      YEAR = {2015},
      NUMBER = {7-8},
      PAGES = {961--984},
      ISSN = {0933-5846},
      MRCLASS = {03E35 (03E55)},
      MRNUMBER = {3416159},
      MRREVIEWER = {Xianghui Shi},
      DOI = {10.1007/s00153-015-0453-8},
      URL = {http://dx.doi.org/10.1007/s00153-015-0453-8},
      PDF={http://boolesrings.org/victoriagitman/files/2015/06/IndestructibleRemarkableCardinals.pdf},
      EPRINT ={1411.2551},
      }

  • Incomparable $\omega_1$-like models of set theory
    • G. Fuchs, V. Gitman, and J. D. Hamkins, “Incomparable $\omega_1$-like models of set theory.” (To appear in {M}athematical {L}ogic {Q}uarterly)  
      @ARTICLE{fuchsgitmanhamkins:omega1models,
      AUTHOR= {Gunter Fuchs and Victoria Gitman and Joel David Hamkins},
      TITLE= {Incomparable $\omega_1$-like models of set theory},
      PDF={http://boolesrings.org/victoriagitman/files/2015/01/incomparableOmega1LikeModels.pdf},
      EPRINT={1501.01022},
      NOTE= {To appear in {M}athematical {L}ogic {Q}uarterly}}

  • 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.  
      @INCOLLECTION{gitmanjohnstone:groundmodels,
      AUTHOR = {Victoria Gitman and Thomas A. Johnstone},
      TITLE = {On ground model definability},
      BOOKTITLE = {Infinity, Computability, and Metamathematics: Festschrift in honour of the 60th birthdays of Peter Koepke and Philip Welch},
      Publisher = {College publications},
      YEAR = {2014},
      series = {Series:Tributes},
      Address = {London, GB},
      PDF={http://boolesrings.org/victoriagitman/files/2013/11/groundmodels.pdf},
      EPRINT ={1311.6789}
      }

  • 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, iss. 9, pp. 934-952, 2015.  
      @ARTICLE{gitmancody:eastonramsey,
      AUTHOR= {Victoria Gitman and Brent Cody},
      TITLE= {Easton's theorem for {R}amsey and strongly {R}amsey cardinals},
      PDF={http://boolesrings.org/victoriagitman/files/2014/12/eastonramsey.pdf},
      EPRINT ={1209.1133},
      JOURNAL = {Annals of Pure and Applied Logic},
      VOLUME = {166},
      NUMBER ={9},
      YEAR = {2015},
      PAGES = {934-952},
      }

  • What is the theory ZFC without power set?
    • V. Gitman, J. D. Hamkins, and T. Johnstone, “What is the theory $\mathsf {ZFC}$ without power set?,” Mlq math. log. q., vol. 62, iss. 4-5, pp. 391-406, 2016.  
      @ARTICLE{zfcminus:gitmanhamkinsjohnstone,
      AUTHOR = {Gitman, Victoria and Hamkins, Joel David and Johnstone, Thomas
      A.},
      TITLE = {What is the theory {$\mathsf {ZFC}$} without power set?},
      JOURNAL = {MLQ Math. Log. Q.},
      FJOURNAL = {MLQ. Mathematical Logic Quarterly},
      VOLUME = {62},
      YEAR = {2016},
      NUMBER = {4-5},
      PAGES = {391--406},
      ISSN = {0942-5616},
      MRCLASS = {03E30},
      MRNUMBER = {3549557},
      MRREVIEWER = {Arnold W. Miller},
      DOI = {10.1002/malq.201500019},
      URL = {http://dx.doi.org/10.1002/malq.201500019},
      PDF={http://boolesrings.org/victoriagitman/files/2011/10/ZFC-.pdf},
      EPRINT={1110.2430}}

  • 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, pp. 257-283, 2012.  
      @article {apterhamkinsgitman:inner,
      author = {Apter, Arthur and Gitman, Victoria and Hamkins, Joel David},
      affiliation = {Mathematics, The Graduate Center of the City University of New York, 365 Fifth Avenue, New York, NY 10016, USA},
      title = {Inner models with large cardinal features usually obtained by forcing},
      journal = {Archive for Mathematical Logic},
      publisher = {Springer Berlin / Heidelberg},
      issn = {0933-5846},
      keyword = {Mathematics and Statistics},
      pages = {257--283},
      volume = {51},
      issue = {3},
      PDF={http://boolesrings.org/victoriagitman/files/2011/08/innermodels.pdf},
      eprint = {1111.0856},
      doi = {10.1007/s00153-011-0264-5},
      year = {2012}
      }

  • 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, iss. 4, pp. 475-484, 2010.  
      @article {multiverse:gitmanhamkins,
      AUTHOR = {Gitman, Victoria and Hamkins, Joel David},
      TITLE = {A natural model of the multiverse axioms},
      JOURNAL = {Notre Dame J. Form. Log.},
      FJOURNAL = {Notre Dame Journal of Formal Logic},
      VOLUME = {51},
      YEAR = {2010},
      NUMBER = {4},
      PAGES = {475--484},
      PDF={http://boolesrings.org/victoriagitman/files/2011/08/multiverse.pdf},
      EPRINT ={1104.4450},
      ISSN = {0029-4527},
      MRCLASS = {03C62 (03E40 03E99)},
      MRNUMBER = {2741838 (2012b:03099)},
      MRREVIEWER = {Andrzej Ros{\l}anowski},
      DOI = {10.1215/00294527-2010-030},
      URL = {http://dx.doi.org/10.1215/00294527-2010-030},}

  • Ramsey-like Cardinals II
    • V. Gitman and P. D. Welch, “Ramsey-like cardinals II,” The journal of symbolic logic, vol. 76, iss. 2, pp. 541-560, 2011.  
      @ARTICLE{gitman:welch,
      AUTHOR= "Victoria Gitman and Philip D. Welch",
      TITLE= "Ramsey-like cardinals {II}",
      JOURNAL = {The Journal of Symbolic Logic},
      VOLUME = {76},
      YEAR = {2011},
      NUMBER = {2},
      PAGES = {541-560},
      PDF={http://boolesrings.org/victoriagitman/files/2011/08/ramseylikecardinalsii.pdf},
      EPRINT ={1104.4448},
      ISSN = {0022-4812},
      CODEN = {JSYLA6},
      MRCLASS = {03E55},
      MRNUMBER = {2830435 (2012e:03111)},
      MRREVIEWER = {Bernhard A. K{\"o}nig},
      DOI = {10.2178/jsl/1305810763},
      URL = {http://dx.doi.org/10.2178/jsl/1305810763},
      }

  • Ramsey-like cardinals
    • V. Gitman, “Ramsey-like cardinals,” The journal of symbolic logic, vol. 76, iss. 2, pp. 519-540, 2011.  
      @ARTICLE {gitman:ramsey,
      AUTHOR = {Victoria Gitman},
      TITLE = {{R}amsey-like cardinals},
      JOURNAL = {The Journal of Symbolic Logic},
      VOLUME = {76},
      YEAR = {2011},
      NUMBER = {2},
      PAGES = {519-540},
      EPRINT={0801.4723},
      PDF={http://boolesrings.org/victoriagitman/files/2011/08/ramseylikecardinals.pdf},
      ISSN = {0022-4812},
      CODEN = {JSYLA6},
      MRCLASS = {03E55},
      MRNUMBER = {2830415 (2012e:03110)},
      MRREVIEWER = {Bernhard A. K{\"o}nig},
      DOI = {10.2178/jsl/1305810762},
      URL = {http://dx.doi.org/10.2178/jsl/1305810762},
      }

  • Proper and piecewise proper families of reals
    • V. Gitman, “Proper and piecewise proper families of reals,” Mathematical logic quarterly, vol. 55, iss. 5, pp. 542-550, 2009.  
      @ARTICLE {gitman:proper,
      AUTHOR = {Victoria Gitman},
      TITLE = {Proper and Piecewise Proper Families of Reals},
      JOURNAL = {Mathematical Logic Quarterly},
      VOLUME = {55},
      YEAR = {2009},
      NUMBER = {5},
      PAGES = {542-550},
      PDF={http://boolesrings.org/victoriagitman/files/2011/08/properscott.pdf},
      EPRINT ={0801.4368},
      ISSN = {0942-5616},
      MRCLASS = {03E35 (03E40 03H15)},
      MRNUMBER = {2568765 (2011c:03109)},
      MRREVIEWER = {Renling Jin},
      DOI = {10.1002/malq.200810015},
      URL = {http://dx.doi.org/10.1002/malq.200810015},
      }

  • Scott’s problem for proper Scott sets
    • V. Gitman, “Proper and piecewise proper families of reals,” Mlq math. log. q., vol. 55, iss. 5, pp. 542-550, 2009.  
      @article {gitman:scott,
      AUTHOR = {Gitman, Victoria},
      TITLE = {Proper and piecewise proper families of reals},
      JOURNAL = {MLQ Math. Log. Q.},
      FJOURNAL = {MLQ. Mathematical Logic Quarterly},
      VOLUME = {55},
      YEAR = {2009},
      NUMBER = {5},
      PAGES = {542--550},
      ISSN = {0942-5616},
      MRCLASS = {03E35 (03E40 03H15)},
      MRNUMBER = {2568765},
      MRREVIEWER = {Renling Jin},
      DOI = {10.1002/malq.200810015},
      URL = {http://dx.doi.org/10.1002/malq.200810015},
      PDF={http://boolesrings.org/victoriagitman/files/2011/08/scottsets.pdf},
      EPRINT ={0801.4364},
      }

  • 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. (Thesis (Ph.D.)–City University of New York)  
      @book {gitman:dissertation,
      AUTHOR = {Gitman, Victoria},
      TITLE = {Applications of the proper forcing axiom to models of {P}eano
      arithmetic},
      NOTE = {Thesis (Ph.D.)--City University of New York},
      PUBLISHER = {ProQuest LLC, Ann Arbor, MI},
      YEAR = {2007},
      PAGES = {149},
      ISBN = {978-0549-26219-0},
      PDF ={http://boolesrings.org/victoriagitman/files/2014/11/dissertation2.pdf},
      MRCLASS = {Thesis},
      MRNUMBER = {2710923},
      URL =
      {http://gateway.proquest.com/openurl?url_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:dissertation&res_dat=xri:pqdiss&rft_dat=xri:pqdiss:3283199},
      }