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comment Singular in $V$ regular in $HOD$
What are the large cardinals they're using there?
Apr
29
comment Does Con(ZF + Reinhardt) really imply Con(ZFC + I0)?
@Joel: Thanks. "Counterexample" to your statement, mathoverflow.net/questions/237662/… :-)
Apr
29
comment Does Con(ZF + Reinhardt) really imply Con(ZFC + I0)?
@Joel: I know that, which is why this was a comment and not an answer. I was just trying to get a confirmation on my question. Despite having the advisor that I have, large cardinals (and very large cardinals) are still not so deep inside my comfort zone that I can make a remark like the one I made without someone double checking it.
Apr
29
comment Is there an image for you that epitomizes mathematics?
@Todd: abstrusegoose.com/230
Apr
29
comment Does Con(ZF + Reinhardt) really imply Con(ZFC + I0)?
@Joel: Correct me if I'm wrong, but if $\kappa$ is a Reinhardt cardinal, and $\lambda=\sup j^n(\kappa)$, then there is an elementary embedding from $L(V_{\lambda+1})$ to itself. No? So at least as far as ZF is concerned, Reinhardt implies I0.
Apr
28
comment Embedding property of weakly compact cardinals
@Rahman: Thanks for the link, I saw that before posting the question actually. (I must have missed your comment before, sorry)
Apr
28
comment Embedding property of weakly compact cardinals
Thanks Joel. That helps!
Apr
27
revised Embedding property of weakly compact cardinals
Typo.
Apr
27
comment Embedding property of weakly compact cardinals
I referred specifically to compactness, and three other definitions, in my edit.
Apr
27
comment Embedding property of weakly compact cardinals
Yes, that is probably what's going to happen later tonight. I've just arrived after two weeks away, and a lot of things need attention.
Apr
27
comment Embedding property of weakly compact cardinals
That's helpful, but actually that is probably the least helpful equivalent here. But it is helpful!
Apr
27
comment Embedding property of weakly compact cardinals
Okay, I think I see where this is going. Thanks. I'd still be happy to see a reference, but after I'll get settled back at home I'll hunt the reference you pointed to. Thanks.
Apr
27
comment Embedding property of weakly compact cardinals
The embedding in the weakly compact case are already fully elementary. What do you strengthen when you pass from $\Pi_1^1$ to higher levels in the hierarchy?
Apr
27
revised Embedding property of weakly compact cardinals
added 382 characters in body; edited tags
Apr
26
comment Embedding property of weakly compact cardinals
Wait, what is the "obvious" generalization above $\Pi^1_1$?
Apr
26
comment Embedding property of weakly compact cardinals
Thanks, Mohammad. But is there a direct proof anywhere?
Apr
26
asked Embedding property of weakly compact cardinals
Apr
25
comment Nonexistence of generic objects over $L(\mathbb{R})$
I'd be surprised if the answer is positive to this broad case. Perhaps if you consider idealized forcings with "relatively definable" ideals (whatever that might be).
Apr
25
comment Mathematicians with Aphantasia (Inability to Visualize Things in One's Mind)
I don't have aphantasia, but I find it very very hard to visualize some mathematical objects. But not the ones you'd expect: I have no problem visualizing a model of set theory, an infinite dimensional vector space, or convergence in the cofinite topology over $\Bbb Z$. I am having a very hard time imagining, however, a plane moving through a ball, or what are gradients, and what the hell are Lagrange multipliers? Luckily, all those have comfortable formal definitions for me to use as a cushion when I have to.
Apr
22
comment Does Con(ZF + Reinhardt) really imply Con(ZFC + I0)?
@Gro-Tsen: The word "Reinhardt" does not appear in either paper of the Suitable Extender Models.