741 reputation
213
bio website alexanderpruss.com
location United States
age
visits member for 2 years, 8 months
seen May 8 at 17:54

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