561 reputation
1312
bio website colorado.edu/math
location Boulder, CO
age 32
visits member for 4 years, 5 months
seen 1 hour ago
I am a math instructor at the University of Colorado at Boulder. My interests have evolved from proof theory and philosophical concerns about knowledge to the upper reaches of set theory and the large cardinal hierarchy. I also occasionally dabble in combinatorics of the finite sort.

Jul
2
awarded  Curious
Jun
11
comment Are normal ultrafilters generated by conditional closure systems?
@JDH: If I'm thinking of the correct "Solovay's lemma" that was mentioned, I think there is a nice proof at Andres Caicedo's blog.
Jun
10
accepted Stationary sets in HOD
Jun
10
comment Stationary sets in HOD
Right. That was sloppy of me. I'll need to think about your great answer some more. In the meantime, I guess I'm trying to articulate a question about the definability (not necessarily using only ordinal parameters) of clubs and stationary sets.
Jun
10
comment Stationary sets in HOD
@JDH. Thank you for your answer. One interesting fact that I glean from it is that stationary sets are definable, whereas there are club sets that are not not (at least from ordinal parameters). Is this correct? Since you mention the forcing which kills a stationary/co-stationary set, is this the only way to conclude that there are club sets which are not definable, or is there an easier argument to see this?
Jun
10
asked Stationary sets in HOD
May
20
awarded  Fanatic
Feb
25
accepted Elementary Embeddings and Relative Constructibility
Feb
16
comment Antichains and the Knaster Property
@Paul McKenney: Thanks for your comment. I posed the question because I had a deep misunderstanding of the concept and you alerted me to this fact. Thanks!
Feb
16
revised Antichains and the Knaster Property
The background of the question was false and made for a confusing question.
Feb
13
revised Ultrapowers of ultrapowers
added set theory tag
Feb
13
suggested suggested edit on Ultrapowers of ultrapowers
Feb
13
accepted Antichains and the Knaster Property
Feb
13
comment Antichains and the Knaster Property
@MohammadGolshani: Yes, thank you!. I've edited my question.
Feb
13
revised Antichains and the Knaster Property
switched the ordering of my question to make sense
Feb
13
asked Antichains and the Knaster Property
Feb
2
comment What is the definition of a large cardinal axiom?
@Joel and Asaf: given your comments, how would you alter any of the proposed categories? I'm certainly willing to give up the full strength of ZFC, but I'm really not familiar enough with many of its fragments and their respective strength. Is ZFC or its strengthenings simply too strong a base to use when attempting a definition of "large cardinal"?
Feb
2
answered What is the definition of a large cardinal axiom?
Jan
24
comment What is the definition of a large cardinal axiom?
@StevenLandsburg: Couldn't it move toward a consensus? Sites like this provide a deeper and at the same time broader understanding of topics informed by experts working in the field, even if that understanding borders on what might be considered more philosophical concerns. If the only "definitions" of large cardinal are implicitly understood, so be it. But certainly we could benefit from having a single source collecting together some of these implicit "definitions", right?
Jan
24
comment What is the definition of a large cardinal axiom?
I think this is actually an important, if soft, question worthy of discussion by set-theorists with some interest in the subject. There is at least one formal definition that I know of offered by Woodin in part II of his article on CH in the AMS. I don't know if he himself considers the definition there satisfactory, but there doesn't seem to be any consensus on the topic (as far as I can tell).