Skip to main content
MathOverflow

Return to Question

edited body
Source Link
bestian tang
bestian tang
  • 321
  • 1
  • 5

I've read these words: "How many ultra products $∏_Uℕ$ exist up to isomorphism, where $U$ is a non-principal ultrafilter over $ℕ$? If continuum hypothesis(CH) holds, then obviously just one ..."

i don'ydon't know why "obviously" just one? CH just tell the cardinality, not the structral of ultrafilter. even $U_1$ and $U_2$ have same cardinality c, how to make sure their structural can't be different?

where can I find the proof detail or the insight which make this "obvious"?

I've read these words: "How many ultra products $∏_Uℕ$ exist up to isomorphism, where $U$ is a non-principal ultrafilter over $ℕ$? If continuum hypothesis(CH) holds, then obviously just one ..."

i don'y know why "obviously" just one? CH just tell the cardinality, not the structral of ultrafilter. even $U_1$ and $U_2$ have same cardinality c, how to make sure their structural can't be different?

where can I find the proof detail or the insight which make this "obvious"?

I've read these words: "How many ultra products $∏_Uℕ$ exist up to isomorphism, where $U$ is a non-principal ultrafilter over $ℕ$? If continuum hypothesis(CH) holds, then obviously just one ..."

i don't know why "obviously" just one? CH just tell the cardinality, not the structral of ultrafilter. even $U_1$ and $U_2$ have same cardinality c, how to make sure their structural can't be different?

where can I find the proof detail or the insight which make this "obvious"?

corrected title
Link
François G. Dorais
François G. Dorais
  • 44.4k
  • 6
  • 150
  • 233

why Why does CH implies the uniquenessimply that there is a unique ultrapower of non-principal ultrafilter over ℕ$\mathbb{N}$?

Source Link
bestian tang
bestian tang
  • 321
  • 1
  • 5

why CH implies the uniqueness of non-principal ultrafilter over ℕ?

I've read these words: "How many ultra products $∏_Uℕ$ exist up to isomorphism, where $U$ is a non-principal ultrafilter over $ℕ$? If continuum hypothesis(CH) holds, then obviously just one ..."

i don'y know why "obviously" just one? CH just tell the cardinality, not the structral of ultrafilter. even $U_1$ and $U_2$ have same cardinality c, how to make sure their structural can't be different?

where can I find the proof detail or the insight which make this "obvious"?