#settheory — Public Fediverse posts

I'm looking for an intro into set theory for a very non mathematical person. Everything I find uses numbers, sets of sets of sets, and such things.

Did the mathematicians loose their marbles? :-)

I mean, explaining sets using marbles should be an easy way to introduce the concepts. Only if those are understood, it may be sensible to go to Hilberts hotel, Russells paradox, and maybe, just maybe to Cantors diagonal argument.

#math #SetTheory #marbles

Suggestions welcome.

I'm looking for an intro into set theory for a very non mathematical person. Everything I find uses numbers, sets of sets of sets, and such things.

Did the mathematicians loose their marbles? :-)

I mean, explaining sets using marbles should be an easy way to introduce the concepts. Only if those are understood, it may be sensible to go to Hilberts hotel, Russells paradox, and maybe, just maybe to Cantors diagonal argument.

#math #SetTheory #marbles

Suggestions welcome.

I'm looking for an intro into set theory for a very non mathematical person. Everything I find uses numbers, sets of sets of sets, and such things.

Did the mathematicians loose their marbles? :-)

I mean, explaining sets using marbles should be an easy way to introduce the concepts. Only if those are understood, it may be sensible to go to Hilberts hotel, Russells paradox, and maybe, just maybe to Cantors diagonal argument.

#math #SetTheory #marbles

Suggestions welcome.

I'm looking for an intro into set theory for a very non mathematical person. Everything I find uses numbers, sets of sets of sets, and such things.

Did the mathematicians loose their marbles? :-)

I mean, explaining sets using marbles should be an easy way to introduce the concepts. Only if those are understood, it may be sensible to go to Hilberts hotel, Russells paradox, and maybe, just maybe to Cantors diagonal argument.

#math #SetTheory #marbles

Suggestions welcome.

I'm looking for an intro into set theory for a very non mathematical person. Everything I find uses numbers, sets of sets of sets, and such things.

Did the mathematicians loose their marbles? :-)

I mean, explaining sets using marbles should be an easy way to introduce the concepts. Only if those are understood, it may be sensible to go to Hilberts hotel, Russells paradox, and maybe, just maybe to Cantors diagonal argument.

#math #SetTheory #marbles

Suggestions welcome.

Wasn't expecting a set theory round on university challenge - a gift to all three set theorists who watched the episode!

#maths #settheory

RE: https://friendica.world/display/84b6ef2b-1569-fb6a-c9a4-fc9241315409

This topic is too close to my heart for me to find it funny 😅
#math #mathematics #settheory #infinity

RE: https://mastodon.social/@sflorg/116517535576002455

The human behavioral range, filters overlapping data segments by learned, hard encoded, and individual bias...

#BehavioralScience #Scalar #Differential #Equations #DoingTheMath #BehavioralRange #ValueTheory #SetTheory

RE: https://mastodon.social/@sflorg/116517535576002455

The human behavioral range, filters overlapping data segments by learned, hard encoded, and individual bias...

#BehavioralScience #Scalar #Differential #Equations #DoingTheMath #BehavioralRange #ValueTheory #SetTheory

RE: https://mastodon.social/@sflorg/116517535576002455

The human behavioral range, filters overlapping data segments by learned, hard encoded, and individual bias...

#BehavioralScience #Scalar #Differential #Equations #DoingTheMath #BehavioralRange #ValueTheory #SetTheory

Late to the party, but I heart “Rethinking Set Theory”, Tom Leinster’s presentation of ETCS (https://arxiv.org/abs/1212.6543). My natal foundation is higher-order logic, and this is the first time set theory has made any sense to me, other than as a technical device.

Bonus lecture notes: https://webhomes.maths.ed.ac.uk/~tl/ast/ast.pdf

#settheory #etcs #higherorderlogic

Late to the party, but I heart “Rethinking Set Theory”, Tom Leinster’s presentation of ETCS (https://arxiv.org/abs/1212.6543). My natal foundation is higher-order logic, and this is the first time set theory has made any sense to me, other than as a technical device.

Bonus lecture notes: https://webhomes.maths.ed.ac.uk/~tl/ast/ast.pdf

#settheory #etcs #higherorderlogic

Late to the party, but I heart “Rethinking Set Theory”, Tom Leinster’s presentation of ETCS (https://arxiv.org/abs/1212.6543). My natal foundation is higher-order logic, and this is the first time set theory has made any sense to me, other than as a technical device.

Bonus lecture notes: https://webhomes.maths.ed.ac.uk/~tl/ast/ast.pdf

#settheory #etcs #higherorderlogic

Late to the party, but I heart “Rethinking Set Theory”, Tom Leinster’s presentation of ETCS (https://arxiv.org/abs/1212.6543). My natal foundation is higher-order logic, and this is the first time set theory has made any sense to me, other than as a technical device.

Bonus lecture notes: https://webhomes.maths.ed.ac.uk/~tl/ast/ast.pdf

#settheory #etcs #higherorderlogic

So we have { 1, 2 } ∈ Fin₁ ⊆ Fin₁ₐ ⊆ Fin₂ ⊆ Fin₃ ⊆ Fin₄ ⊆ Fin₅ ⊆ Fin₆ ⊆ Fin₇

If a set is in Fin₁ then it is considered finite by all the other definitions.

But since the axiom of choice is equivalent to saying every set can be well-ordered, if we accept it VII-finite sets are equinumerous with a finite ordinal and so Fin₇ ⊆ Fin₁ and so the differences between these definitions collapse and ZF becomes ZFC, which is a widely accepted basis for Set Theory.

My consultation with math resources was inspired by a blog post:

https://www.infinitelymore.xyz/p/what-is-the-infinite

#Metamath #ZFC #SetTheory #AxiomOfChoice #FiniteSet #Infinity

Any #mathematics professors want to take a shot at explaining to someone with say a typical math major undergrad background what the deal is with the recent introduction of exacting and ultraexacting cardinals?

#math #maths #settheory #zfc

https://arxiv.org/abs/2411.11568

Interesting read about #mathematics, #settheory, and #informationtheory from Quanta Magazine, about getting closer to resolving the union-closed conjecture. It references the 1948 paper, “A Mathematical Theory of Communication" from #claudeshannon.

https://www.quantamagazine.org/long-out-of-math-an-ai-programmer-cracks-a-pure-math-problem-20230103/

#GregoryChaitin - Is #Mathematics #Eternal?

https://www.youtube.com/watch?v=KEuylDsONxo

#Philosophy #PhilosophyOfScience #PhilosophyOfMathematics #Science #Math #Maths #Cantor #Ramanujan #SetTheory #God #Spirituality #Beauty #Transcendence #Numbers #Contradiction #Logic #Poincaré #Poincare #Euler #CloserToTruth #RobertKuhn

Begriffsschrift (1879), is one of the first manuscripts on #SymbolicLogic. As such, it literally invents a new language to describe the subjects the author, #GottlobFrege, wants to introduce. And this notation is very unlike what we see in math before or after this.

So I will list some theorems adapted (by me, circa 2020) from #Frege with proper set-theoretical bounds.

#SetTheory #Logic #Metamath

Alright, future engineers!
The **Union** of sets A & B (A U B) is all elements in A *or* B.
Ex: A={1,2}, B={2,3}. A U B = {1,2,3}.
Pro-Tip: Think 'OR' for Union. It includes everything from either set!
#SetTheory #DiscreteMath #STEM #StudyNotes

Take a set, 𝑥. Is it finite or infinite? Well what definition do you use?

① ∃𝑦 ∈ ω₀ 𝑥 ≈ 𝑦 ; There is a natural number, 𝑦, such that you may may map 𝑦 one-to-one onto the set 𝑥, enumerating each of its members. So 𝑥 is finite for the same reason { 1, 2, 3 } is finite.

② ¬ ∃𝑧 ∈ (On ∖ ω₀) 𝑥 ≈ 𝑧 ; There is no such infinite ordinal, 𝑧, such that you may map 𝑧 one-to-one onto the set 𝑥. So 𝑥 is finite because ω₀, the smallest infinite ordinal, cannot be mapped 1-to-1 into it.

Do ① and ② say the same thing?

Obviously, ① implies ② in all cases for if it didn't there would be at least one natural number, 𝑦, which may be used to enumerate at least one infinite ordinal, 𝑧.

But does ② imply ①? If ② doesn't imply ① then there must be sets which can't be be placed side-by-side with any infinite ordinal and yet can't be placed side-by-side with any finite ordinal. In short, there must be sets which can't be well-ordered. But the axiom of choice says all sets may be well-ordered, even if it doesn't provide a recipe.

Not only does the axiom of choice say all sets can be well-ordered and thus ② implies ①, but assuming ② implies ① is equivalent to the axiom of choice. It was invented by Zermelo for this purpose and so that ①, ②, and 6 alternative definitions of "finite set" all mean the same thing.

The axiom of choice is basically saying the border between finite and infinite has nothing trapped in it.

#AxiomOfChoice #OrdinalNumbers #SetTheory #FiniteSet

Alright, future engineers!

A **Cartesian Product (A x B)** is the set of all ordered pairs (a,b) where a∈A & b∈B.
Ex: A={1,2}, B={x,y} => A x B = {(1,x),(1,y),(2,x),(2,y)}.
Pro-Tip: It's how you model all possible pairs across two sets!

#DiscreteMath #SetTheory #STEM #StudyNotes

Alright, future engineers!

A **Power Set** P(S) is the set of *all* possible subsets of set S. Ex: If `S = {1, 2}`, then `P(S) = {{}, {1}, {2}, {1, 2}}`. Pro-Tip: Its size (cardinality) is always `2^|S|`!

#SetTheory #DiscreteMath #STEM #StudyNotes

Alright, future engineers! **Cartesian Product (A x B)** creates all ordered pairs (a,b) where 'a' is from set A & 'b' from set B.

Ex: A={1,2}, B={x,y}. A x B = {(1,x), (1,y), (2,x), (2,y)}.

Pro-Tip: Essential for understanding relations and functions – think of it as building a grid of possibilities!

#DiscreteMath #SetTheory #STEM #StudyNotes

Alright, future engineers!
The **Power Set** of a set A is the set of *all* possible subsets of A. Ex: For A={1,2}, P(A) = {{}, {1}, {2}, {1,2}}.
Pro-Tip: If a set has 'n' elements, its power set will always have 2^n elements. Handy for combinatorics!

#SetTheory #DiscreteMath #STEM #StudyNotes

Set Intersection (A ∩ B) finds elements common to *both* sets A & B. Ex: A={1,2,3}, B={2,3,4} -> A ∩ B = {2,3}. Pro-Tip: Think of it as AND – an element must be in A AND in B to be in the intersection!

#DiscreteMath #SetTheory #STEM #StudyNotes

I have the greatest admiration for the theorems and proofs of transfinite set theory, what we've called Cantor's transfinite set theory.

I taught it for years, wrote restatements for my students, and wrote a piece viewing it in the perspective of historical thinking about the infinite.
http://nrs.harvard.edu/urn-3:HUL.InstRepos:3715468

Now I've learned that #Cantor deliberately suppressed the role of #Dedekind in some of his work, particularly the proof that the set of real numbers is larger than the sets of natural and rational numbers. This was the first glimpse of the infinite hierarchy of infinite cardinalities.
https://www.quantamagazine.org/the-man-who-stole-infinity-20260225/

Cantor had the first germ of the proof, so props for that. But Dedekind helped him clarify it and Cantor published the clarified version without credit to Dedekind. I respect the math as much as ever but am now dealing with a serious case of flawed-hero syndrome.

First, make amends. Kudos to Dedekind. Second, give thanks. Kudos to the sleuths who turned up the empirical evidence of Cantor's #plagiarism -- Emmy Noether, Ivor Grattan-Guinness, José Ferreirós, and (decisively) Demian Goos.

Also thanks to Joseph Howlett for the Quanta article summarizing the evidence -- and in passing for calling Leopold #Kronecker an ideologue. Exactly!

#Infinity #Mathematics #SetTheory

@unnick @CenTdemeern1 Another angle to see this would be set theroy; like a normal d6 would conform to the set {1, 2, 3, 4, 5, 6} while your special die with only one face showing seven would be the set {7}. A true zero-sided set would therefor be the empty set ∅ / {}.

Now we define the action of rolling to picking a random entry of the set... however I'm unsure what this means in the case of ∅:

• We could argue that randomly picking is reducing the set to just a set by throwing our all other numbers, this would mean that a d6 would be reduced to {4} (if you roll a 4); in the same manner, rolling ∅ would mean the result still is ∅ since we cant reduce further.

• On the other hand we can go the normal way and say it's not reducing the set but producing a number, but numbers themselv can be represented using sets by converting the number (i.e. 3) into a series of nested sets build by their previous components:

0 = ∅
1 = {0} = {∅}
2 = {0,1} = {∅, {∅}}
3 = {0,1,2} = {∅, {∅}, {∅, {∅}}}

(Called Zermelo-Fraenkel set theory)

... so ultemately I think the right answer would be ∅? (I'm not a mathematician, I just like nerdy stuff and happen to know about set theory bc. of uni, but I'm happy to be proven wrong)

#settheory #mathematics

Every well-ordered set is isomorphic to an ordinal. Common notion, for example see Introduction to https://arxiv.org/abs/2409.07352

⊢((𝐴∈V∧𝑅We𝐴)↔∃𝑓(dom𝑓∈On∧𝑓IsomE,𝑅(dom𝑓,𝐴)))

\[ \vdash ( ( A \in \mathrm{V} \wedge R \mathrm{We} A ) \leftrightarrow \exists f ( \mathrm{dom} f \in \mathrm{On} \wedge f \mathrm{Isom} \mathrm{E} , R ( \mathrm{dom} f , A ) ) ) \]

Every well-ordered set is isomorphic to
a unique ordinal.

⊢((𝐴∈V∧𝑅We𝐴)↔∃!𝑜∈On∃𝑓∈(𝐴↑ₘ𝑜)𝑓IsomE,𝑅(𝑜,𝐴))

\[ \vdash ( ( A \in \mathrm{V} \wedge R \mathrm{We} A ) \leftrightarrow \exists{!} o \in \mathrm{On} \exists f \in ( A \uparrow_\mathrm{m} o ) f \mathrm{Isom} \mathrm{E} , R ( o , A ) ) \]

We can phrase the Axiom of Choice as "Every set injects into an ordinal."

⊢(CHOICE↔∀𝑥∃𝑜∈On𝑥≼𝑜)

\[ \vdash ( \mathrm{CHOICE} \leftrightarrow \forall x \exists o \in \mathrm{On} x \preccurlyeq o ) \]

#math #metamath #SetTheory #WellOrdering #OrdinalNumbers

@FishFace
Here's the paper from 1958:

http://matwbn.icm.edu.pl/ksiazki/fm/fm46/fm4611.pdf

Where reference [7] is
https://eudml.org/doc/213059 where 𝔖 is defined to have ur-Elements

Prior work:
(𝔖 or ZF) + AC ⊢ Fin₁ = Fin₁ₐ = Fin₂ = Fin₃ = Fin₄ = Fin₅ = Fin₆ = Fin₇

EScbO = the axiom "Every set can be (linearly, strictly) ordered"

Theorem 1 is
(𝔖 or ZF) ⊢ Fin₁ ⊆ Fin₁ₐ ⊆ Fin₂ ⊆ Fin₃ ⊆ Fin₄ ⊆ Fin₅ ⊆ Fin₆ ⊆ Fin₇

Theorem 2 is
(𝔖 or ZF) ⊢ ( R Orders A ∧ A ∈ Fin₂ ) → A ∈ Fin₁

Theorem 3 is
(𝔖 or ZF) + EScbO ⊢ Fin₁ = Fin₁ₐ = Fin₂

Theorem 4 is
𝔖 + EScbO ⊢ Fin₁ ≠ Fin₃

Theorem 5 is
𝔖 + EScbO ⊢ Fin₃ ≠ Fin₄

Theorem 6 is
𝔖 + EScbO ⊢ Fin₄ ≠ Fin₅

Theorem 7 is
𝔖 + EScbO ⊢ Fin₅ ≠ Fin₆

Theorem 8 is
𝔖 + EScbO ⊢ Fin₆ ≠ Fin₇

Theorem 9 is
𝔖 ⊢ Fin₁ ≠ Fin₁ₐ

Theorem 10 is
(𝔖 or ZF) ⊢ ( Fin₁ₐ = Fin₂ → Fin₁ = Fin₁ₐ )

Theorem 11 is
𝔖 ⊢ Fin₁ₐ ≠ Fin₂

As it so happens, I know of a proof:
ZF + CC ⊢ Fin₁ = Fin₄

Where the axiom of Countable Choice, CC, can be expressed as ⊢ (𝑥 ≈ ω → ∃𝑓∀𝑧 ∈ 𝑥 (𝑧 ≠ ∅ → (𝑓‘𝑧) ∈ 𝑧))

See https://us.metamath.org/mpeuni/fin41.html where CC is used only for the line ⊢ (ω ≼ 𝑥 ↔ ¬ 𝑥 ≺ ω)

So good guess!

And JDH on Substack isn't requiring payments which disadvantages him with respect to SEO, so please share the links. #AxiomOfCountableChoice #AxiomOfChoice #SetTheory #CountableChoice

A New Bridge Links the Strange Math of Infinity to Computer Science https://www.wired.com/story/a-new-bridge-links-the-strange-math-of-infinity-to-computer-science/ #Science/PhysicsandMath #SetTheory #Science

A New Bridge Links the Strange Math of Infinity to Computer Science

https://web.brid.gy/r/https://www.wired.com/story/a-new-bridge-links-the-strange-math-of-infinity-to-computer-science/

Happy birthday of set theory, for all those who celebrate!

On December 7, 1873, Georg Cantor (https://en.wikipedia.org/wiki/Georg_Cantor) wrote a letter (https://www.aleph1.info/?call=Puc&permalink=cd1_Briefe_Z4) to Richard Dedekind in which he showed that there are more real numbers than integers and that therefore different kinds of infinity exist. Cantor's proof at this time is not the “diagonalisation” proof that is now usually given.

December 7, 1873 is also the 50th birthday of Leopold Kronecker (https://en.wikipedia.org/wiki/Leopold_Kronecker), which is ironic, given the heavy conflicts they would have about set theory.

The birthday of set theory is usually celebrated with a birthday cake that has ℵ₀ candles on it, but you can take fewer if you don't have the space for them. 🕯️

#SetTheory #Mathematics #HistoryOfMathematics #HistoryOfScience #GeorgCantor #LeopoldKronecker

Readings shared November 24, 2025. https://jaalonso.github.io/vestigium/posts/2025/11/25-readings_shared_11-24-25 #CompSci #CoqProver #ITP #LeanProver #Logic #Math #Physics #SetTheory #TypeTheory

Set theory with types. ~ Lawrence Paulson. https://lawrencecpaulson.github.io//2025/11/21/Typed_Set_Theory.html #Logic #Math #CompSci #SetTheory #TypeTheory

"Like parsley in Greek food: Elementary set theory and the case for DM1" by Siddharth Bhaskar (https://dblp.org/pid/170/0077.html) got accepted at SIGCSE TS 2026.

https://sigcse2026.sigcse.org/details/sigcse-ts-2026-Papers/164/Like-parsley-in-Greek-food-Elementary-set-theory-and-the-case-for-DM1

#SIGCSE #setTheory #CSEducation #math #discreteMath #computerScience

I am now finishing an expository article on variants of Axiom of Choice and weakenings of the Tychonoff Theorem. the following is what might be contained in the introduction of the paper. It is my attempt to explain the significance of the study of this subject to general or set-theoretic topologists who are going to be the main readers of the RIMS Kôkûroku volume the article is going to appear.

#数学 #集合論 #mathematics #settheory #topology

Readings shared April 13, 2025. https://jaalonso.github.io/vestigium/posts/2025/04/13-readings_shared_04-13-25 #AI #ATP #Coq #FunctionalProgramming #Haskell #ITP #IsabelleHOL #LLMs #LeanProver #Mace4 #Math #Prover9 #SetTheory

A brain dump from Matrix Dreams: A better-defined series of sets

I’ve been pondering the weird collection of sets I cooked up in this post. In this post, I’d like to take a crack at defining the sets.

I’m going to bow to my ego and call these the MattSets. MattSet Prime is the set of all integers found in all the other MattSets.

MattSet0 is the set of all powers of two. As such, it is an even set. All members of MattSet0 are even.

There are two types of MattSets – even and not even (odd) sets. Each set is generated from the set before it.

MattSet1 is the first odd set. It is the set of all the numbers when multiplied by three that the numbers in the previous set is one more than. Another way to say this is – make an intermediary set of all members of MattSet0 (MattSetn-1 in general form) that are one more than a multiple of three. Take all the members of this intermediary set and apply the function (x-1)/3. This will give you MattSet1 which is an odd set.

MattSet2 is two be an even set. MattSet2 is the set of all integers that are twice a member of MattSet1 (MattSetn-1 in general form).

Each subsequent set is generated in the same way such that MattSets with even indexes are even numbers and MattSets with odd indexes are odd.

As far as I have, so far, tested each odd MattSet has half the number of members as the preceding even MattSet.

In theory: As n approaches infinity, the size of the MattSetn approaches 0. At least I think that it does.

The question I am looking to answer is does MattSet Prime contain all the positive integers? If I can’t prove that one way or the other, is there anything interesting about these sets that can be proved?

A better-defined series of sets, 8th October 2024, by Matt

Note: I’m not sure I was all that clear the first time, but only integer values can be members of these sets.

You could add some other series of (empty) sets for completion. MattSetnx. A member of the MattSetnx is an even number not found in MattSet0 that is twice the value of a MattSet0 member. MattSetn+1x. Would be all the even numbers not in the preceding sets that are twice the value of one of the previous nx sets. In theory, all MattSetnx sets are empty, as twice a power of two is another power of two.

Prove me wrong.

• websitematrixdreams.com
• websitebrid.gy

#maths #MatrixDreams #MattSet #setTheory #syndicated #MyVeryBestContent

@paysmaths
Any scientist or mathematician who claims the existence of a deity to support a ‘proof’ has left the path of reason. #Maths #Mathematics #Math #Cantor #SetTheory

#Veritasium - #Math's #FundamentalFlaw

https://www.youtube.com/watch?v=HeQX2HjkcNo&ab_channel=Veritasium

#RussellParadox #BertrandRussell #Philosophy #PhilosophyOfLanguage #PhilosophyOfLogic #Logic #Math #Maths #Mathematics #SetTheory #Sets #Predicates #Subjects #Paradox #LogicalParadox #Contradiction #Contradictions #Incompleteness #IncompletenessTheorem #Goedel #Hilbert

#JeffreyKaplan - #RussellsParadox - A simple #Explanation of a profound #Problem

https://www.youtube.com/watch?v=ymGt7I4Yn3k&ab_channel=JeffreyKaplan

#BertrandRussell #Philosophy #PhilosophyOfLanguage #PhilosophyOfLogic #Logic #Math #Maths #Mathematics #SetTheory #Sets #Predicates #Subjects #Paradox #LogicalParadox #Contradiction #Contradictions #Incompleteness #IncompletenessTheorem #Goedel #Hilbert

How Long is #Now? - An #Introduction to #Metaphysics

https://www.youtube.com/watch?v=8HzIlKe--NU

#exurb1a #Philosophy #PhilosophyOfScience #Science #PhilosophyOfTime #Time #Induction #Logic #SetTheory #Physics #Biology #ParticlePhysics #ManifestImage #Entropy #Matter #Energy #Mind #Being

(3/7)
- Large cardinal axioms in #SetTheory are often equivalent to asserting that there exists *well-founded* models with various properties, which gives you access to more induction.
- In Predicative Arithmetic by Edward Nelson (https://web.math.princeton.edu/~nelson/books.html) it's shown that by severely weakening induction and then considering what numbers still satisfy inductive properties, you can get a system that might be acceptable in #ultrafinitism.

#MathInduction

Lecturas compartidas el 25 de marzo de 2024. https://jalonso.substack.com/lecturas-compartidas-el-25-de-marzo #AI #CategoryTheory #FormalVerification #ITP #IsabelleHOL #KRR #LLMs #Math #Mathematica #Python #SetTheory

Readings shared March 23, 2025. https://jaalonso.github.io/vestigium/posts/2025/03/23-readings_shared_03-23-25 #Agda #Coq #FunctionalProgramming #HOL_Light #Haskell #ITP #IsabelleHOL #LeanProver #Math #Mizar #SetTheory

@LeoTsai14 While they do not actually call it so, set theoreticians do a lot of work in a category in which the objects are the models of set theory and the arrows are the elementary embeddings (https://en.wikipedia.org/wiki/Elementary_equivalence#Elementary_embeddings) between them.
Models of (ZFC-like) set theories have the interesting property that the maps between them are to some amount determined by the mappings between their classes of ordinals: If this map is an isomorphism, the whole map is one (https://en.wikipedia.org/wiki/Critical_point_(set_theory)).
You may also have a look at inner model theory (https://en.wikipedia.org/wiki/Inner_model_theory), I think.

#SetTheory #ModelTheory #MathematicalLogic #Categories

Make the integers
as Russian dolls.

#SixWordStories
#SixWordTheorems

#MathematicalPoetry
#SetTheory
#ZermeloFrankel #vonNeumann

Russel's Paradox

"is not true of itself"
— Is it true of itself?

If it is, then it isn't.
If it isn't, then it is.

#JeffreyKaplan #BertrandRussel #SetTheory
https://www.youtube.com/watch?v=ymGt7I4Yn3k

Hi fam, have a fulfilling day! Ayliean‬ ‪@ayliean.bsky.social‬: an account worth following. #SharingIsCaring #sharingisthenewlearning #MathArtMarch 7th #Howmany out of n and how many #reflections? #LEGO #sculpture #settheory #binomialcoefficients #abstractart #physics #refraction #PhotographyIsArt

RE: https://bsky.app/profile/did:plc:omyr27fmzj3phbagch4sqyub/post/3ljqrcjpc622a