Skip to main content
MathOverflow

Return to Question

edited tags
Link
Joel David Hamkins
Joel David Hamkins
  • 236.5k
  • 44
  • 777
  • 1.4k
replaced http://mathoverflow.net/ with https://mathoverflow.net/
Source Link
Community Bot
Community Bot
  • 1
  • 2
  • 3

I asked herehere about "large powerset axioms" and to my delight, learned that such axioms are being taken seriously. I've been toying with them ever since. My favourite is: "The continuum function is injective, and for all infinite cardinals $\kappa$ we have that $2^\kappa$ is weakly inaccessible," since this is easy to understand yet implies the existence of a rich universe of cardinal arithmetic. But it occurs to me that before toying any further, I should really find out whether or not this axiom is consistent with ZFC.

So, does anyone know a contradiction from this axiom? And if not, are any large cardinal axioms known to imply its consistency? I could not find the answers in the linked articles, nor do I really know where to start looking.

I asked here about "large powerset axioms" and to my delight, learned that such axioms are being taken seriously. I've been toying with them ever since. My favourite is: "The continuum function is injective, and for all infinite cardinals $\kappa$ we have that $2^\kappa$ is weakly inaccessible," since this is easy to understand yet implies the existence of a rich universe of cardinal arithmetic. But it occurs to me that before toying any further, I should really find out whether or not this axiom is consistent with ZFC.

So, does anyone know a contradiction from this axiom? And if not, are any large cardinal axioms known to imply its consistency? I could not find the answers in the linked articles, nor do I really know where to start looking.

I asked here about "large powerset axioms" and to my delight, learned that such axioms are being taken seriously. I've been toying with them ever since. My favourite is: "The continuum function is injective, and for all infinite cardinals $\kappa$ we have that $2^\kappa$ is weakly inaccessible," since this is easy to understand yet implies the existence of a rich universe of cardinal arithmetic. But it occurs to me that before toying any further, I should really find out whether or not this axiom is consistent with ZFC.

So, does anyone know a contradiction from this axiom? And if not, are any large cardinal axioms known to imply its consistency? I could not find the answers in the linked articles, nor do I really know where to start looking.

Source Link
goblin GONE
goblin GONE
  • 3.8k
  • 18
  • 39

Consistency of: "The continuum function is injective, and for all infinite cardinals $\kappa$ we have that $2^\kappa$ is weakly inaccessible."

I asked here about "large powerset axioms" and to my delight, learned that such axioms are being taken seriously. I've been toying with them ever since. My favourite is: "The continuum function is injective, and for all infinite cardinals $\kappa$ we have that $2^\kappa$ is weakly inaccessible," since this is easy to understand yet implies the existence of a rich universe of cardinal arithmetic. But it occurs to me that before toying any further, I should really find out whether or not this axiom is consistent with ZFC.

So, does anyone know a contradiction from this axiom? And if not, are any large cardinal axioms known to imply its consistency? I could not find the answers in the linked articles, nor do I really know where to start looking.