inacessible cardinals

[hayate]

one inacessible cardinal weakly compact is high 1-A and woodin give you boundless?

 

[Vietthai96]

With my limited knowledge
Inaccessible = High 1-A
Mahlo = baseline tier 0
Woodin is several layers into tier 0

 

[hayate]

but this cardinais is inacessibles

 

[Makoto500]

Not sure if weakly inaccessible is high1a but maybe?

Weakly compacts are tier 0.

As for woodin it's in the high line of 0.

 

[Makoto500]

but this cardinais is inacessibles

All of this cardinals are indeed inaccessible cardinals.

(Or atleast falls into the category of inaccessible or being inaccessible.)

 

[Makoto500]

Not sure if weakly inaccessible is high1a but maybe?

Weakly compacts are tier 0.

As for woodin it's in the high line of 0.

Mahlo is also tier 0 the baseline of it.
(Im talking about normal strong mahlo.
Kinda not sure on weakly mahlo though.)

 

[KakarotGoku]

All of this cardinals are indeed inaccessible cardinals.

(Or atleast falls into the category of inaccessible or being inaccessible.)

Don't you mean mahlo?

 

[Makoto500]

Don't you mean mahlo?

Hmm? This cardinals fall into the category of inaccessible and mahlo.

Also mahlo is a inaccessible as well and both are identical anyways.

 

[KakarotGoku]

but this cardinais is inacessibles

As cat said.

Weakly compacts are around the baseline of tier 0 and Woodin is in the highline of 0.

And all of this are a form of inaccessible and mahlo cardinals it seems.

 

[TheDivineHost]

A weakly inaccessible cardinals is one that cannot be reached by taking successor cardinals, strongly inaccessible is when it can't be reached by taking powersets.

You can form even stronger axioms by assuming they also satisfy some Ramsey theoretic condition.

For example having a weakly inaccessible k, requiring that every 2 colouring of [k]^2 has a k sized homogenous subset gives the weakly compact cardinals.

 

[KakarotGoku]

A weakly inaccessible cardinals is one that cannot be reached by taking successor cardinals, strongly inaccessible is when it can't be reached by taking powersets.

You can form even stronger axioms by assuming they also satisfy some Ramsey theoretic condition.

For example having a weakly inaccessible k, requiring that every 2 colouring of [k]^2 has a k sized homogenous subset gives the weakly compact cardinals.

I think the question here is that if weakly compacts and woodin are tier 0 or High1-A.

 

[TheDivineHost]

I think the question here is that if weakly compacts and woodin are tier 0 or High1-A.

0

 

[KakarotGoku]

0

Seems like it's already answered then.

(About 3 times now actually.)