Skip to primary content
Skip to secondary content

Joel David Hamkins

mathematics and philosophy of the infinite

Joel David Hamkins

Main menu

  • Home
    • About
    • My Curriculum Vita
    • Contact
    • Comment Board
  • Publications
    • Publication list
    • Recent publications
    • Publications by topic
      • Automorphism towers
      • Infinitary computability
      • Infinitary utilitarianism
      • Large cardinals
    • My Research Collaborators
  • Talks
    • Talks
    • Recent and Upcoming Talks
    • Videos
  • Appointments and Grants
    • About Me
    • My Academic Appointments
    • Grants and Awards
  • Teaching
    • About My Courses
  • Students
    • About My Graduate Students
    • List of My Graduate Students
  • Mathematical Shorts
  • Math for Kids

Tag Archives: NWO

Modal logics in set theory, NWO grants, 2006 – 2008

Posted on April 30, 2006 by Joel David Hamkins
Reply

Modal logics in set theory, (with Benedikt Löwe), Nederlandse Organisatie voor Wetenschappelijk (B 62-619), 2006-2008.

Share:

  • Click to share on X (Opens in new window) X
  • Click to share on Facebook (Opens in new window) Facebook
  • Click to share on Reddit (Opens in new window) Reddit
  • Click to share on WhatsApp (Opens in new window) WhatsApp
  • Click to email a link to a friend (Opens in new window) Email
  • Click to print (Opens in new window) Print
  • More
  • Click to share on LinkedIn (Opens in new window) LinkedIn
  • Click to share on Tumblr (Opens in new window) Tumblr
  • Click to share on Pocket (Opens in new window) Pocket
  • Click to share on Pinterest (Opens in new window) Pinterest
Posted in Grants and Awards | Tagged Amsterdam, NWO | Leave a reply

Infinitely More

Proof and the Art of Mathematics, MIT Press, 2020

Buy Me a Coffee

Recent Comments

  • Joel David Hamkins on Lectures on Set Theory, Beijing, June 2025
  • Joel David Hamkins on Lectures on Set Theory, Beijing, June 2025
  • Mohammad Golshani on Lectures on Set Theory, Beijing, June 2025
  • Jack Edward Tisdell on Lectures on Set Theory, Beijing, June 2025
  • Joel David Hamkins on Skolem’s paradox and the countable transitive submodel theorem, Leeds Set Theory Seminar, May 2025

JDH on Twitter

My Tweets

RSS Mathoverflow activity

  • Answer by Joel David Hamkins for Do independent collections of infinitely many buttons and infinitely many switches exist in models other than V=L?
    Yes, there are many models of ZFC with infinite independent families of buttons and switches. For example, if you start with any model of V=L, and then switch the switches quite a lot, but not push any of the buttons, then you still have a family of independent buttons and switches, but now you don't […]
  • Comment by Joel David Hamkins on Is every external downshifting elementary embedding $j$ with $j(x)=j[x]$, an automorphism?
    Yes, I have now edited.
  • Comment by Joel David Hamkins on Is every external downshifting elementary embedding $j$ with $j(x)=j[x]$, an automorphism?
    I am a little unclear about whether the embeddings arising in Friedman's theorem need be elementary from $M$ to $M$. I believe the proof uses back-and-forth realizing types in such a way that they would be, but I wonder whether this just follows easily from the fact that $j$ is an isomorphism of $M$ with […]
  • Answer by Joel David Hamkins for Is every external downshifting elementary embedding $j$ with $j(x)=j[x]$, an automorphism?
    Let me omit the need for any extra assumption beyond consistency of ZFC. In fact, every countable computably saturated model of ZFC is a counterexample. If $M$ is a countable computably saturated model of ZFC, then there will be an ordinal $\theta$ in $M$ for which $V_\theta^M\prec M$. One can simply realize the type describing […]
  • Comment by Joel David Hamkins on Is the set of theorems of a PA + “PA is inconsistent” equivalent to the halting set?
    Yes, I agree, the method is very general.
  • Comment by Joel David Hamkins on Is it possible to transform a statement of unsolvabilty to an equivalent one by using a bounded universal quantifier
    If your polynomial $P$ would allow several variables instead of just one, then the answer is negative. But you are interested in the case where there is only one $x$?
  • Answer by Joel David Hamkins for Is the set of theorems of a PA + “PA is inconsistent” equivalent to the halting set?
    It is a very nice question. I interpret the theme of the question as: how much can we rely on the theorems of $\newcommand\PA{\text{PA}}\newcommand\Con{\text{Con}}\PA+\neg\Con(\PA)$? In fact, I shall show that a simple transformation for $\Sigma_1$ assertions allows us to fully rely on it. In particular, the answers to both questions are affirmative. The proof will […]
  • Answer by Joel David Hamkins for A question about Borel code
    The property of $r$ being a Borel code is a $\Pi^1_1$ property, since everything about it is easy arithmetic except asserting that the tree you are labeling is well-founded, and that brings it up to $\Pi^1_1$. If $r$ is indeed a Borel code, then to say that $x\in A_r$ is complexity $\Delta^1_1(r)$, since you can […]

Meta

  • Log in
  • Entries feed
  • Comments feed
  • WordPress.org

Subscribe to receive update notifications by email.

Tags

  • absoluteness
  • buttons+switches
  • CH
  • chess
  • computability
  • continuum hypothesis
  • countable models
  • definability
  • determinacy
  • elementary embeddings
  • forcing
  • forcing axioms
  • games
  • GBC
  • generic multiverse
  • geology
  • ground axiom
  • HOD
  • hypnagogic digraph
  • indestructibility
  • infinitary computability
  • infinite chess
  • infinite games
  • ITTMs
  • kids
  • KM
  • large cardinals
  • Leibnizian models
  • maximality principle
  • modal logic
  • models of PA
  • multiverse
  • open games
  • Oxford
  • philosophy of mathematics
  • pluralism
  • pointwise definable
  • potentialism
  • PSC-CUNY
  • supercompact
  • truth
  • universal algorithm
  • universal definition
  • universal program
  • Victoria Gitman
Proudly powered by WordPress