Reputation
518
Top tag
Next privilege 1,000 Rep.
Create new tags
Badges
2 9
Newest
 Critic
Impact
~3k people reached

  • 0 posts edited
  • 0 helpful flags
  • 15 votes cast
3h
comment Is the critical point of an embedding of a model of set theory inaccessible in it?
Ah sure time travel and Hebrew, I will study that next. :D For now, I'm learning Spanish and set theory.
4h
comment Is the critical point of an embedding of a model of set theory inaccessible in it?
Oh right! I didn't notice the hole either, thinking of the argument to prove diamond in L with the elementary substructure of $L_{\omega_1}$. Couldn't we argue like this: Take the least $\kappa$ with $M\models \, \kappa$ is inaccessible. Then in $V_{\kappa}^M$ ZFC+"there is no inaccessible" holds. The compactness theorem + transitivation should imply there is an uncountable transitive model of ZFC+no inaccessibles (argue with constant symbols $c_{\alpha}$ for $\alpha<\omega_1$ and sentences $c_{\alpha}\neq c_{\beta}$ for $\alpha <\beta<\omega_1$).
1d
comment Is the critical point of an embedding of a model of set theory inaccessible in it?
In understand, but I didn't know yet if the most general form of question has an example, although I thought there is probably one, I didn't know how difficult it is, or if restrictions wil make it harder to answer. I also thought about asking : What if $M$ is a model of ZFC minus powerset and $\kappa$ is the largest cardinal in $M$. Anyway, I got some nice answers, so I'm happy.
1d
comment Is the critical point of an embedding of a model of set theory inaccessible in it?
Ok, I see. Then I'll be able to go from there. Thanks again for the swift response. :) It seems like there is a science about this kind of forcing. A course on large cardinals in hebrew, that's pretty specific. :)
1d
comment Is the critical point of an embedding of a model of set theory inaccessible in it?
Thanks all the same.
1d
comment Is the critical point of an embedding of a model of set theory inaccessible in it?
Thank you. I'll have to read into these 3 (with Camilo's) examples. It'll be fun I guess. About the first example, which forcing do you mean when you say "we can force over M"? Or is that better left as an exercise to figure out?
1d
comment Is the critical point of an embedding of a model of set theory inaccessible in it?
Ah, I knew this part and I have read about amenable ultrafilters in the context of iterated ultrapowers. I looked in "The Higher Infinite" by Kanamori again and he points out you only need models of ZFC without the powerset axiom to define the M-ultrafilter. (in case M and N have the same powerset of $\kappa$)
1d
comment Is the critical point of an embedding of a model of set theory inaccessible in it?
This is the simplest example to me. Thank you.
Aug
30
comment What's wrong with this proof of Schröder-Bernstein theorem?
The argument works, it is the same that can be found for example in Jech's "Set Theory". I think "analyze" just means checking it is correct here.
Aug
30
comment Closeness of measures on a cardinal
I checked that for a two-step iteration by a normal measure, $V\to M_1 \to M_2$, the $k$ obtained from the map from $V$ to $M_2$ is the same as the map from $M_1$ to $M_2$. And the embedding of $V$ to $M_2$ is an ultrapower embedding for a product ultrapower on $\kappa\times \kappa$, but we could make that into an ultrapower on $\kappa$ with Gödel pairing. So in this case the critical point of $k$ is $j_1(\kappa)$ when $j_1:V\to M_1$ is the ultrapower embedding for the normal measure on $\kappa$.
Aug
29
comment Looking for extender axioms
Haha, well English is not my native language, maybe the title sounds weird.
Aug
29
comment Row rank$=$Column rank
Try computing $A\cdot e_i$ where $e_i$ is the vector with a 1 at the ith place and zeroes at all other places. Then use that every n-dimensional vector is a linear combination of the $e_i$ for $1\leq i \leq n$.
Aug
29
comment $\omega_1$-closedness and fullness for $\searrow$ $\omega$-sequences
What comes to my mind concerning the first proof is: In the assumption needed to apply "fullness", we need a name $\rho_n$ for every $n<\omega$, but in your proof, you only use one name $\rho$. (*) is correct, but it doesn't enable you to apply the consequence for "full".
Aug
29
comment How many of each ticket were sold in one day?
Oh sorry. I didn't realize the question was that old. My bad.
Aug
29
comment How many of each ticket were sold in one day?
It's not given that on day one and two the same number of each type of ticket was sold. So, different notation like $a_1,a_2$ etc. would be much clearer.
Aug
28
comment Closeness of measures on a cardinal
Thank you for the contribution, Miha. Could you explain why $cof(cp(k))\leq \kappa^+$ ? I understand the rest.
Aug
28
comment Limit of a recurrence
Take the limit on both sides of the equation for $b_{n+1}$. For the limit of the right side, use that square root is continuous.
Feb
21
comment Homology isomorphism of $H_n(S^d\times X)$ and $H_{n-1}(S^{d-1}\times X)$
Thanks. Maybe I made a mistake copying the statement.
Dec
20
comment $cov(null)$ in a Cohen model
Thanks, I will look at that.
Dec
19
comment $cov(null)$ in a Cohen model
Could you point me where to find a proof of this?