Jason Chen

Cesare Straffelini, Sebastiano Thei
Higher Solovay Models
https://arxiv.org/abs/2507.19129

Vladimir Kanovei, Vassily Lyubetsky
Notes on the equiconsistency of ZFC without the Power Set axiom and 2nd order PA
https://arxiv.org/abs/2507.11643

Yale Philosophy offers a course on “Formal Philosophical Methods” — a broad introduction to probability, logic, formal semantics, etc.

Instructor Calum McNamara has now made all materials for the course (78 pages) freely available

static1.squarespace.com/static/6255f...

It should be June 2025 instead of June 2023 (as it currently states in the blog opening), right?

Maybe it's a nice baby logic exercise to observe how the negation of "you can make it anywhere" is *not* "you can't make it anywhere" - one of those cautionary tales of the mismatch between the logical form and the natural language (surface) syntax ;)

I built a little Shiny app that shows how often various words were used in 20 prominent philosophy journals from 1980-2019.

bweatherson.shinyapps.io/t20-graphs/

James Cummings, Yair Hayut, Menachem Magidor, Itay Neeman, Dima Sinapova, Spencer Unger
The tree property on long intervals of regular cardinals
https://arxiv.org/abs/2505.08118

My publisher wants alt text for my tikz figures, which is a good idea. They asked for a Word file, absurd, but here is my latex solution. I wrote \alttext macro. Place \alttext{alt text} at end of every tikz picture. Resulting pdf shows alt text with mouseover on figure.

That's amazing. Great win for the set theory community!

that's a lot of ground to cover! (Yes pun intended...) These lectures will be for how many days?

ZML - Zeitschrift für Mathematische Logik und Grundlagen der Mathematik ZML: Zeitschrift für Mathematische Logik und Grundlagen der Mathematik is an electronic Diamond Open Access research journal in mathematical logic publishing original research papers in all areas of m...

I'm excited to join the editorial board of a new diamond open access journal in mathematical logic:

ZML: Zeitschrift für Mathematische Logik und Grundlagen der Mathematik
zml.international

The open letter of the editors of ZML can be found online on the webpage.

The true Kuhnian paradigm-shifts all and only those who don't paradigm-shift their own paradigm.

Your favorite theorem? ;)

A great pleasure to be nominated on the APA Committee on Non-Academic Careers. Looking forward to contributing back to the broader philosophical community in the next three years!

YouTube video by DorFuchs Die Ableitung vom Sinus ist der Kosinus (Mathe-Song)

I don't speak German, and neither do my calculus students, but even so I think this is one of the best explanations of the derivative of sine and cosine I've ever seen.

Also, it's a bop that won't get out of my head.
#mathsky #iTeachMath

www.youtube.com/watch?v=tSov...

oh right, because N contains M to begin with... Thanks!

I remember Groszek has a way to force (from a model M of ZFC+CH) a minimal failure of CH, in the sense that any model N s.t. M⊆N⊆M[G] is a model of CH but M[G] is not. An uncountable such M[G] will witness the failure of the countable transitive submodel proposition, right?

Ah, I see, so the thought is that Löwenheim-Skolem gives you well-founded submodel, and Mostowski collapse gives you the transitive isomorph, but the Mostowski collapse might not be a submodel of the original model (only that it embeds in it via the anti-collapse map).

What is "the countable transitive submodel proposition"? Is it just the claim that every transitive model of (say) ZFC has a countable transitive (proper) submodel?

I made an awesome pun in Chinese about the Fubini property today. Too bad it won't translate...

Really reassuring that there's still a place where people enjoy talking about ideals, especially in today's society

Really great stuff, wishing more mathematicians would spend some time writing about their fields like this. Set Theory and the Analyst is another great read with similar themes: arxiv.org/abs/1801.09149

An uncountable measurable subset of $\Bbb R$ containing no nonempty perfect set $\newcommand\R{\Bbb R}$Assuming the axiom of choice, is there an uncountable Lebesgue-measurable subset $S$ of $\R$ that contains no nonempty perfect set? Of course, such a set $S$, if it exists, ...

A natural (uncountable) set of reals without a perfect subset, whose measurability can be shown via forcing! mathoverflow.net/a/484096

The hero we need but don't deserve

See also the discussion in this MO thread: mathoverflow.net/a/482756
This is what makes set theory immensely appealing for me - properly mathematical pursuits inevitably run up against issues beyond the space between Theorem and QED: standards of refutation and acceptance, criteria for evidence, etc

I'll be giving a talk at the ASL-APA 2025 Spring meeting (Feb. 27-March 1, 2025), on the subtly different uses of the Church-Turing Thesis (and relatives) in actual mathematical practice.

But I can see how the last point could be as controversial as the choiceless LCs themselves ;) Of course, none of this undercuts the (very) surprising discovery of compatibility of AC and refuting V=HOD. Either way, exciting times for (philosophy of) set theory!

That's fair. I guess my ground-not-shakier point boils down to this: without Con. strength payoff, there's only conceptual gains (familiar notion/techniques etc), but at this point the new notions are about as familiar as the Reinhardts and Berkeleys, so if the new proof is good then so is the old.

I guess my lingering itch is just this: in terms of refuting the WHH, what does this paper add on top of what we already know? We already have such a refutation; so now we have to say a bit about why this new refutation is better or more convincing.

That being said, I think this opens up a lot of exciting new doors: if AC is no longer the culprit, then there might be hope in understanding the choiceless cardinals (maybe in relation to the exactings) in such a way that the earlier refutations of WHH can be seen as being already good enough.