The Continuum Hypothesis and the search for Mathematical Infinity, W. Hugh Woodin

Does the Continuum Hypothesis have an answer? This question is pointed out by professor W. Hugh Woodin. He admits that 15 years ago he thought it was false. Has his opinion changed? You can see from this lecture.

William Hugh Woodin is an American mathematician and set theorist at Harvard University. He has made many notable contributions to the theory of inner models and determinacy. A type of large cardinal, the Woodin cardinal, bears his name.

[carlkuss]

He show himself to be a person who has very thoroughly thought about these matters, and knows his stuff inside out. I have listened to this (on a cd) a number of times. Every time I get a little more out. I love his simplicity and straightforwardness.

[henrywebster]

A brilliant lecture, given by one of the giants of set theory.

[Doppeganger]

"Maybe in the end the ultimate skeptic is correct that the entire conception of the universe of sets is a complete fiction, it's just intuition gone wild, it's a human creation, that there's no truth there." Most important sentence of this entire lecture bar none.

[ez_is_bloo]

I don't understand this at all yet. Might need to re-watch it multiple times. Don't mind me documenting my progress here '-'.

[declup]

"If you assume V = L as your axiom, there are no measurable cardinals.... In fact, the modern view is there are no genuine large cardinals." But then: "The axiom V = L is false -- because the whole point of set theory is to understand infinity; you can't deny large cardinals." Why not accept that there is an interpretation such that there are no large cardinals? Must large cardinals exist because they're the target of scrutiny by set theory?

[WriteRightMathNation]

I really am enjoying this presentation by Hugh, but what in the world did he say at 8:45???? It sounds like "so...hau won mon wan".

[MrBorceivanovski]

Perfect presentation! Only I am missing the definition of the "Good Set" ?

[khongdong]

Perhaps this CH-Infinity conundrum could be more fruitfully examined by looking at the shadow of ZFC's _syntactical_ axioms as casted, silhouetted on FOL _without_ equality where:

a) The FOL= logical symbol = is replaced by a non-logical counterpart, say, =' (which introspectively, subjectively could be interpreted as being equivalent/equal in probability of existence)

b) any function expression would be casted as a corresponding relation.

Just saying.

[TheMaxtimax]

How does Cohen's work show that GCH is consistent with ZFC ?

[ZeroG]

Now prove that feeding the output into the input of a function that maps a cardinal of order n to one of order 3n+1 when n is odd and n/2 when n is even, produces eventually a cardinal of order one when the function iterates indefinitely on any cardinal of order n.

[AlbertoLopezisnotit]

So Elegant Exposed and Beautiful!! ...Very very very... very .... very very .... very very Very ... Nice!!  .... ✾ .... ☻

[tulgatbolderdene]

i just proved the Continuum Hypothesis but this margin of comment section is too small to fit in the proof

[joseville]

6:40 why is CH a statement about V_{\omega + 2}?

[liijio]

Proving continuum hypothesis, proving inconsistency in ZFC, constructing ZFC from naive set specification, resolving Russell's paradox, constructing infinite number system, construct and ensure overall consistent mathematical universe and developing arithmetic system - edition 8
May 2024
DOI: 10.13140/RG.2.2.21713.75361
LicenseCC BY-NC-ND 4.0

[garryseville]

He sounds like one of the teachers in Ferris Bueller's Day Off..

[michaelmilbocker]

pure genius, some needs to let susskind know about this

[JimOverbeckgenius]

I began to create Non-Cantorian set theory without tertium exclusi in 1960 + infinite sentences & transfinite fractions. I substituted Grandi's series [= Fourier-Bolzano series] for natural number isomorphs & attended 3 universities, winning a scholarship in the Foundations of Mathematics along the way. Professor Geoffrey Kneebone sent my work to 12 Oxbridge etc maths academics & I was outed age 17 as a super-genius by UK Mil Intel & equated with WJ Sidis. On experiencing Theosis I destroyed my book The Theory of Intermediate Transfinite Cardinals, but wrote out 2 notebooks summing up my results for Geoffrey. I followed Sidis' example of going to ground but my writings on maths, logic, philosophy, theology, psychology, art ETC now comprise probably the largest illustrated volume[s] since Leonardo & I continue writing and doing artworks. I painted a large triptych called The Madness of Mathematics, featuring mathematicians who went insane or whom I consider as such. There is a short film, made only a couple of days ago, called Why theosis is genius, which gives a short explanation of my ideas on Infinity [go to Minds.com at JimiTheos aka Jim Overbeck] + there is a film by a BBC editor-director on YouTube The Lost Genius.

[RedShiftedDollar]

"Assuming that the axioms are true then we can prove that ... is false" and "assuming the axioms are true then we can prove that ... is true". Well, scrutinize the axioms! The axiom of infinite and the axiom of choice are not self evident and if they turn out to be false or indeterminate then every proof built on them will either crumble or be suspect at best.

[naimulhaq]

Vw is infinite, it is the set of all finite sets. The continuum hypothesis remains undefined, therefore 'unknown'.

[getaa]

Brilliant but am I the only one who think- is not qualified enough to understand this video completely?