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.

]]>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 ]]>