Hanul Jeon
@hanuljeon95.bsky.social
A doctoral student at Cornell. Interested in logic and set theory. he/him.
Homepage: https://hanuljeon95.github.io
Homepage: https://hanuljeon95.github.io
I am looking for logicians who may be interested in reviewing my thesis draft. There is no need to check every part of my draft.
November 21, 2025 at 6:21 PM
I am looking for logicians who may be interested in reviewing my thesis draft. There is no need to check every part of my draft.
Reposted by Hanul Jeon
어제 조사 해놔서 놀랍지는 않지만 보니까 짜증이 난다. 망할 콘크리트공화국 이기주의자들아
November 12, 2025 at 10:55 PM
어제 조사 해놔서 놀랍지는 않지만 보니까 짜증이 난다. 망할 콘크리트공화국 이기주의자들아
I think I once saw Anton Freund saying something about Renrui Qi's preprint about the Laver table on FOM, but I could not find it. Perhaps I recalled a hallucination.
November 8, 2025 at 10:25 PM
I think I once saw Anton Freund saying something about Renrui Qi's preprint about the Laver table on FOM, but I could not find it. Perhaps I recalled a hallucination.
Reposted by Hanul Jeon
'아무튼 공황과 침체는 안된다고' 이러면서 유동성을 공급한 결과는 그 유동성으로 소시오패스를 세계 최고의 부자로 만들었고, 이 스노우볼이 굴러가서 수억 수십억명이 고통받고 수십 수백만명이 사망하는 세상을 만들었다. 비둘기들은 본인들이 벌인 일에 대한 자각이 있는지 궁금하다.
자본주의도 민주주의도 이제 황혼을 지나고 있다는 생각이 계속 든다.
자본주의도 민주주의도 이제 황혼을 지나고 있다는 생각이 계속 든다.
October 29, 2025 at 2:45 AM
'아무튼 공황과 침체는 안된다고' 이러면서 유동성을 공급한 결과는 그 유동성으로 소시오패스를 세계 최고의 부자로 만들었고, 이 스노우볼이 굴러가서 수억 수십억명이 고통받고 수십 수백만명이 사망하는 세상을 만들었다. 비둘기들은 본인들이 벌인 일에 대한 자각이 있는지 궁금하다.
자본주의도 민주주의도 이제 황혼을 지나고 있다는 생각이 계속 든다.
자본주의도 민주주의도 이제 황혼을 지나고 있다는 생각이 계속 든다.
The debate on this question reminded me of what I thought before: Type theory can better force a meaning of a sentence through its syntax, so when we ask about the conservativity between set theory and type theory, we should ask about the conservativity of type-theoretic statements.
t.co/cNGFQBJLoO
t.co/cNGFQBJLoO
https://mathoverflow.net/a/91055/48041
t.co
October 23, 2025 at 4:28 AM
The debate on this question reminded me of what I thought before: Type theory can better force a meaning of a sentence through its syntax, so when we ask about the conservativity between set theory and type theory, we should ask about the conservativity of type-theoretic statements.
t.co/cNGFQBJLoO
t.co/cNGFQBJLoO
Junk theorems in set theory are not a bug but a feature.
October 23, 2025 at 12:43 AM
Junk theorems in set theory are not a bug but a feature.
Good googologists must be logicians (the converse does not hold)
October 23, 2025 at 12:08 AM
Good googologists must be logicians (the converse does not hold)
I think Girard's beta cut elimination theorem is essentially cut elimination via operator controlled derivations since we can think of a dilator as an operator taking an ordinal and returning the closure under operators the dilator encodes.
October 22, 2025 at 11:01 PM
I think Girard's beta cut elimination theorem is essentially cut elimination via operator controlled derivations since we can think of a dilator as an operator taking an ordinal and returning the closure under operators the dilator encodes.
The entrance door of logician's hell has a plaque with a single word "Π¹₃"
October 20, 2025 at 2:41 AM
The entrance door of logician's hell has a plaque with a single word "Π¹₃"
Googologists should refrain from making and naming random large countable ordinals for no reason.
I am quite skeptical of how many googologists have even tried to learn Gentzen's ordinal analysis, where the story about recursive ordinal systems started.
I am quite skeptical of how many googologists have even tried to learn Gentzen's ordinal analysis, where the story about recursive ordinal systems started.
October 19, 2025 at 6:40 PM
Googologists should refrain from making and naming random large countable ordinals for no reason.
I am quite skeptical of how many googologists have even tried to learn Gentzen's ordinal analysis, where the story about recursive ordinal systems started.
I am quite skeptical of how many googologists have even tried to learn Gentzen's ordinal analysis, where the story about recursive ordinal systems started.
I learned that every non-standard model of IE1 contains an initial segment satisfying PA. It really sounds like a low-level version of Ville's lemma, which says every ill-founded ω-model of weak set theory (probably Ø-provident set theory) contains an initial segment satisfying KP.
October 16, 2025 at 2:46 PM
I learned that every non-standard model of IE1 contains an initial segment satisfying PA. It really sounds like a low-level version of Ville's lemma, which says every ill-founded ω-model of weak set theory (probably Ø-provident set theory) contains an initial segment satisfying KP.
I hated infinitary types in the proof of projective determinacy when I learned it first time.
Now I think infinitary types are an unavoidable feature of Woodin cardinals.
Now I think infinitary types are an unavoidable feature of Woodin cardinals.
October 13, 2025 at 12:04 AM
I hated infinitary types in the proof of projective determinacy when I learned it first time.
Now I think infinitary types are an unavoidable feature of Woodin cardinals.
Now I think infinitary types are an unavoidable feature of Woodin cardinals.
BTW I found my idea about connecting rudimentary set theory and ACA0 turned out to be wrong. I re-checked Taranovsky's claimed proof, and his idea only produces how to generate an ω-model of one from the other.
October 12, 2025 at 9:09 PM
BTW I found my idea about connecting rudimentary set theory and ACA0 turned out to be wrong. I re-checked Taranovsky's claimed proof, and his idea only produces how to generate an ω-model of one from the other.
One of the main features of set theory as a foundational theory is its cumulative nature. Set theory, in particular, combined with fine-structural machinery, allows fine control in each cumulative hierarchy that often has a role in calibrating the strength of theories.
October 12, 2025 at 9:07 PM
One of the main features of set theory as a foundational theory is its cumulative nature. Set theory, in particular, combined with fine-structural machinery, allows fine control in each cumulative hierarchy that often has a role in calibrating the strength of theories.
I am thinking about the possibility that the number of arguments of a predilator can be… functorially variable, so it takes a linear order A first, then takes an A-indexed family of linear orders, then returns a linear order.
September 17, 2025 at 1:57 AM
I am thinking about the possibility that the number of arguments of a predilator can be… functorially variable, so it takes a linear order A first, then takes an A-indexed family of linear orders, then returns a linear order.
One misconception(?) about the zero sharp is that it "makes" ω₁ inaccessible in L. I think it is not a good POV.
To see why, let us go below: Lat us think of ZFC⁻ (= ZFC without powerset) plus "There is the largest cardinal."
To see why, let us go below: Lat us think of ZFC⁻ (= ZFC without powerset) plus "There is the largest cardinal."
April 19, 2025 at 11:12 PM
One misconception(?) about the zero sharp is that it "makes" ω₁ inaccessible in L. I think it is not a good POV.
To see why, let us go below: Lat us think of ZFC⁻ (= ZFC without powerset) plus "There is the largest cardinal."
To see why, let us go below: Lat us think of ZFC⁻ (= ZFC without powerset) plus "There is the largest cardinal."
In this paper, we defined an alternative way to rank the strength of theories via β-models called the β-rank, and established its basic properties.
We proved that the supremum of the β-rank of theories in the language of set theory is ω1, and the same for the language of SOA if we assume V=L.
We proved that the supremum of the β-rank of theories in the language of set theory is ω1, and the same for the language of SOA if we assume V=L.
Hanul Jeon, Patrick Lutz, Fedor Pakhomov, James Walsh
Ranking theories via encoded $\beta$-models
https://arxiv.org/abs/2503.20470
Ranking theories via encoded $\beta$-models
https://arxiv.org/abs/2503.20470
March 31, 2025 at 10:30 AM
In this paper, we defined an alternative way to rank the strength of theories via β-models called the β-rank, and established its basic properties.
We proved that the supremum of the β-rank of theories in the language of set theory is ω1, and the same for the language of SOA if we assume V=L.
We proved that the supremum of the β-rank of theories in the language of set theory is ω1, and the same for the language of SOA if we assume V=L.
I constructed a measurable dilator from Martin's proof of 𝚷¹₂-Determinacy in this work.
What is a measurable dilator? In short, it is a dilator analogue of a measurable cardinal. A universal dilator is a dilator embedding every countable dilator, and a measurable dilator is given as follows.
What is a measurable dilator? In short, it is a dilator analogue of a measurable cardinal. A universal dilator is a dilator embedding every countable dilator, and a measurable dilator is given as follows.
March 18, 2025 at 9:20 AM
I constructed a measurable dilator from Martin's proof of 𝚷¹₂-Determinacy in this work.
What is a measurable dilator? In short, it is a dilator analogue of a measurable cardinal. A universal dilator is a dilator embedding every countable dilator, and a measurable dilator is given as follows.
What is a measurable dilator? In short, it is a dilator analogue of a measurable cardinal. A universal dilator is a dilator embedding every countable dilator, and a measurable dilator is given as follows.
Some silly post: ZF does not prove there is a regular cardinal. But we can also prove that an inaccessible cardinal (i.e., a cardinal κ s.t. V_κ models second-order ZF) is regular without choice.
Thus there are two ways to supply regular cardinals: Choice or Large cardinals.
Thus there are two ways to supply regular cardinals: Choice or Large cardinals.
January 29, 2025 at 10:01 AM
Some silly post: ZF does not prove there is a regular cardinal. But we can also prove that an inaccessible cardinal (i.e., a cardinal κ s.t. V_κ models second-order ZF) is regular without choice.
Thus there are two ways to supply regular cardinals: Choice or Large cardinals.
Thus there are two ways to supply regular cardinals: Choice or Large cardinals.
In this paper, I tried to answer the proof-theoretic meaning of the value of proof-theoretic dilator (PTD) for non-recursive ordinals and demonstrate the connection b/w PTD and Pohlers' characteristic ordinals.
January 22, 2025 at 6:14 AM
In this paper, I tried to answer the proof-theoretic meaning of the value of proof-theoretic dilator (PTD) for non-recursive ordinals and demonstrate the connection b/w PTD and Pohlers' characteristic ordinals.
Is it correct to say M_n^# is the sharp for the inner model with n Woodin cardinals?
January 21, 2025 at 11:16 AM
Is it correct to say M_n^# is the sharp for the inner model with n Woodin cardinals?
Using large cardinal axioms to compare the strength of theories is like describing hardness via the Mohs scale; We name some specific theories representing the strength in the form of a large cardinal axiom and reduce various statements to them.
January 21, 2025 at 10:44 AM
Using large cardinal axioms to compare the strength of theories is like describing hardness via the Mohs scale; We name some specific theories representing the strength in the form of a large cardinal axiom and reduce various statements to them.
Reposted by Hanul Jeon
jealous
MBC now confirms the president was arrested 10:33 am (13 minutes ago)
January 15, 2025 at 1:53 AM
jealous
Today is the end of Korean logic day. Three days are both long and short for a conference.
January 15, 2025 at 3:06 AM
Today is the end of Korean logic day. Three days are both long and short for a conference.