So I don’t regard this as a “typo”. But perhaps I’m missing something?

(Meanwhile, I have corrected the link; thanks very much for that.)

]]>Thanks for the slides. So far (have not read part slide 30 yet), I really enjoyed reading them.

]]>The article say is no nontrivial embedding j: WF-> WF in ZFC^-f, and the post in mathoverflow say is no X->X in ZFC^-f, so you mean is no Reinhardt and Berkeley cardinal in ZFC^-f?

And I want to know more existence for nontrivial embedding about Kunen inconsistency in ZFC^-f:

M->WF,

WF->M,

M->HOD,

HOD->M and V≠HOD(M),

HOD->HOD,

WF->HOD,

HOD->WF

M->X,

X->M

X: The proper class of all sets

M: Any definable class

Thank you.

]]>Accepted, July 2019.]]>

Eduard Hau (1807–1888), and the digital image is public domain. There is a rich collection of paintings of art gallery interiors in the WikiMedia commons at https://commons.wikimedia.org/wiki/Category:Paintings_of_interiors_of_art_galleries.]]>

this is just a couple of words related to this profound study.

Sorry for taking your time.

I don’t have in hands the ND paper, so whatever follows is related only to the 1501.01918 version.

1. Theorem 4.6 (perhaps by Groszek and/or Laver) was somewhat sharpened in Golshani-K-Lyubetsky, MLQ, 63, No. 1–2, 19–31 (2017): there is a CCC extension

$L[a,b]$ of $L$ by a pair of reals $a,b$, such that 1) the Vitali (or $E_0$) classes A of a

and B of b are different (countable) sets, 2) A and B are OD-indiscernible in $L[a,b]$,

and 3) $A\cup B$ is lightface $\Pi^1_2$ (the lowest possible).

2. Question 4.12 on p 12, its meaning is somewhat elusive. We assume that any OD-algebraic set is OD, and we want to know whether for any two OD sets $x\ne y$, if

$y$ is parameter-free algebraic wrt $x$ then $x$, $y$ are necessarily parameter-free discernible. Is this the idea or I am taking it wrong?

Best

Vladimir]]>

https://doi.org/10.1007/s11856-018-1677-1]]>

Accepted, January 2019.]]>

Accepted, December 2018.]]>

Accepted, September 2018.]]>

The book by Hindman&Strauss has a section on filters and compactifications in a later chapter — that might be suitable for 2).

]]>Possibly relevant is my October 2004 sci.math post “Generalized Quantifiers” (URLs below). FYI, the Math Forum version has a lot of strange formatting errors. See also Brian Thomson’s 1985 book “Real Functions”, and see Thomson’s earlier 2-part survey Derivation bases on the real line (which contain examples and side-detours not in his book).

google sci.math URL:

https://groups.google.com/forum/#!msg/sci.math/rhZEhXynVLQ/MI0MJ0ZQIvoJ

Math Forum sci.math URL:

http://mathforum.org/kb/message.jspa?messageID=3556191

Regarding Moving around every few years for postdocs would be exhausting

, I wholeheartedly agree! Every such decision has pros and cons. They are usually not obvious at the outset. Moreover, they change over time. The lesson I learned though my own course is that every decision is right, at least at the time you make it, and there is never any point regretting it later on… Just keep on doing what you do best all the time!

We went on to look at the paradoxical situations that arise when someone gets a positive test result for a rare disease. Should they be worried? If the test is 99% accurate, but the disease occurs in say, 1 in million, then a positive result is not so worrisome: in million people, there will be about 1 true positive result, and about 10,000 false positives, since 1% of a million is 10,000. So the odds that you’ve actually got the disease, given that you tested positive, is 1 in 10,000.

But your situation is completely different! It would be as though we had calculated the odds of getting HHHTTT, and then when I actually flipped the coin on stage, i actually got the same pattern HHHTTT. Totally weird! And very unlikely. But you know, if it wasn’t that, it would have been some other totally unlikely thing, like getting all green lights, or all red lights, or getting the serial number 123456 on your receipt at Starbucks.

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