bio | website | alexanderpruss.com |
---|---|---|
location | United States | |
age | ||
visits | member for | 2 years, 11 months |
seen | May 8 at 17:54 | |
stats | profile views | 405 |
Professor of Philosophy, Baylor University
Mar
23 |
comment |
How many subsets of $[0,1)$ are there modulo null sets?
@Asaf: It's a bit strange to me, too. I would have expected countable or dependent choice would be all that's needed to prove that there are $c$ Borel sets (and thanks for the catch that $c^2=c$). Maybe we should just try to write out one of the standard proofs very carefully. (No time right now for me.) |
Mar
20 |
revised |
Finitely additive measures on $\mathbb Z_2^\omega$ with invariance and independence constraints
added 10 characters in body |
Mar
20 |
answered | Consequences of ZF+“all subsets of reals are Lebesgue measurable” |
Mar
20 |
comment |
How many subsets of $[0,1)$ are there modulo null sets?
Actually it seems to. The Consequences of AC page says that 8 (Countable Choice) is true and 363 ($2^c$ Borel sets) is false in $\cal M5(\aleph)$ and $\cal M38$. |
Mar
20 |
comment |
How many subsets of $[0,1)$ are there modulo null sets?
Does it use anything beyond countable choice? |
Mar
20 |
accepted | How many subsets of $[0,1)$ are there modulo null sets? |
Mar
20 |
comment |
How many subsets of $[0,1)$ are there modulo null sets?
Agreed, though there are questions about what values for the cardinality are options without AC. (E.g., if all sets are measurable then we get $\le c^2$, assuming that the proof that there are $c$ Borel sets goes through without AC.) |
Mar
20 |
comment |
How many subsets of $[0,1)$ are there modulo null sets?
Thanks! The existence of a set $S$ with the requisite properties (well, or the equivalent claim on the square) also follows from Sierpinski's 1938 partition of the square into perfect sets such that any choice of one element of each of the perfect sets gives a set with full outer measure: eudml.org/doc/213031 |
Mar
19 |
awarded | Nice Question |
Mar
19 |
asked | How many subsets of $[0,1)$ are there modulo null sets? |
Sep
26 |
awarded | Yearling |
Sep
24 |
awarded | Autobiographer |
Jul
21 |
revised |
Embedding probability spaces in the completion of $[0,1]^K$
cleanup |
Jul
17 |
revised |
Embedding probability spaces in the completion of $[0,1]^K$
need completion for lifting |
Jul
17 |
revised |
Embedding probability spaces in the completion of $[0,1]^K$
added 52 characters in body |
Jul
16 |
revised |
Embedding probability spaces in the completion of $[0,1]^K$
replace "finite measure" with "probability" for clarity |
Jul
16 |
asked | Embedding probability spaces in the completion of $[0,1]^K$ |
Jul
8 |
answered | Products of Boolean algebras and probability measures thereon |
Jul
2 |
awarded | Curious |
May
19 |
revised |
Finitely additive measures on $\mathbb Z_2^\omega$ with invariance and independence constraints
added 1156 characters in body |