- Nonlinearity and illfoundedness in the hierarchy of large cardinal consistency strength
[bibtex key=”Hamkins:Nonlinearity-in-the-hierarchy-of-large-cardinal-consistency-strength”] arXiv:2208.07445 Abstract. Many set theorists point to the linearity phenomenon in the hierarchy of consistency strength, by which natural theories tend to be linearly ordered and indeed well ordered by consistency strength. Why should it be linear? In …
- Nonlinearity in the hierarchy of large cardinal consistency strength
This is currently a draft version only of my article-in-progress on the topic of linearity in the hierarchy of consistency strength, especially with large cardinals. Comments are very welcome, since I am still writing the article. Please kindly send me …
- Categorical large cardinals and the tension between categoricity and set-theoretic reflection
[bibtex key=”HamkinsSolberg:Categorical-large-cardinals”]
- The Vopěnka principle is inequivalent to but conservative over the Vopěnka scheme
[bibtex key=Hamkins:The-Vopenka-principle-is-inequivalent-to-but-conservative-over-the-Vopenka-scheme]
- Large cardinals need not be large in HOD
[bibtex key=ChengFriedmanHamkins2015:LargeCardinalsNeedNotBeLargeInHOD]
- Strongly uplifting cardinals and the boldface resurrection axioms
[bibtex key=HamkinsJohnstone2017:StronglyUpliftingCardinalsAndBoldfaceResurrection]
- Resurrection axioms and uplifting cardinals
[bibtex key=HamkinsJohnstone2014:ResurrectionAxiomsAndUpliftingCardinals]
- Superstrong and other large cardinals are never Laver indestructible
[bibtex key=BagariaHamkinsTsaprounisUsuba2016:SuperstrongAndOtherLargeCardinalsAreNeverLaverIndestructible]
- The least weakly compact cardinal can be unfoldable, weakly measurable and nearly $\theta$-supercompact
[bibtex key=CodyGitikHamkinsSchanker2015:LeastWeaklyCompact]
- A multiverse perspective on the axiom of constructiblity
[bibtex key=Hamkins2014:MultiverseOnVeqL]
- Moving up and down in the generic multiverse
[bibtex key=HamkinsLoewe2013:MovingUpAndDownInTheGenericMultiverse]
- Well-founded Boolean ultrapowers as large cardinal embeddings
[bibtex key=HamkinsSeabold:BooleanUltrapowers]
- Singular cardinals and strong extenders
[bibtex key=ApterCummingsHamkins2013:SingularCardinalsAndStrongExtenders]
- Inner models with large cardinal features usually obtained by forcing
[bibtex key=ApterGitmanHamkins2012:InnerModelsWithLargeCardinals]
- What is the theory ZFC without power set?
[bibtex key=”GitmanHamkinsJohnstone2016:WhatIsTheTheoryZFC-Powerset?”]
- Generalizations of the Kunen inconsistency
[bibtex key=HamkinsKirmayerPerlmutter2012:GeneralizationsOfKunenInconsistency]
- Indestructible strong unfoldability
[bibtex key=HamkinsJohnstone2010:IndestructibleStrongUnfoldability]
- Tall cardinals
[bibtex key=Hamkins2009:TallCardinals]
- The proper and semi-proper forcing axioms for forcing notions that preserve $\aleph_2$ or $\aleph_3$
[bibtex key=HamkinsJohnstone2009:PFA(aleph_2-preserving)]
- Large cardinals with few measures
[bibtex key=ApterCummingsHamkins2006:LargeCardinalsWithFewMeasures]
- Extensions with the approximation and cover properties have no new large cardinals
[bibtex key=Hamkins2003:ExtensionsWithApproximationAndCoverProperties]
- Exactly controlling the non-supercompact strongly compact cardinals
[bibtex key=ApterHamkins2003:ExactlyControlling]
- A simple maximality principle
[bibtex key=Hamkins2003:MaximalityPrinciple]
- Indestructibility and the level-by-level agreement between strong compactness and supercompactness
[bibtex key=ApterHamkins2002:LevelByLevel]
- Indestructible weakly compact cardinals and the necessity of supercompactness for certain proof schemata
[bibtex key=ApterHamkins2001:IndestructibleWC]
- The wholeness axioms and $V=\rm HOD$
[bibtex key=Hamkins2001:WholenessAxiom]
- The lottery preparation
[bibtex key=Hamkins2000:LotteryPreparation]
- Book review of The Higher Infinite, Akihiro Kanamori
[bibtex key=Hamkins2000:BookReviewKanamori]
- Gap forcing: generalizing the Lévy-Solovay theorem
[bibtex key=Hamkins99:GapForcingGen]
- Universal indestructibility
[bibtex key=ApterHamkins99:UniversalIndestructibility]
- Superdestructibility: a dual to Laver's indestructibility
[bibtex key=HamkinsShelah98:Dual]
- Small forcing makes any cardinal superdestructible
[bibtex key=Hamkins98:SmallForcing]
- Destruction or preservation as you like it
[bibtex key=Hamkins98:AsYouLikeIt]
- Canonical seeds and Prikry trees
[bibtex key=Hamkins97:Seeds]
- Fragile measurability
[bibtex key=Hamkins94:FragileMeasurability]
- Lifting and extending measures; fragile measurability
[bibtex key=Hamkins94:Dissertation]
- A class of strong diamond principles
[bibtex key=Hamkins:LaverDiamond]
Joel David Hamkins
mathematics and philosophy of the infinite
