Science Talk

tango · Guest

(1) There is an F-sigma-delta additive subgroup of R namely G = {x in
R | limit (n! * pi * x) exists}.

Question: What about the existence of such groups at the higher F
levels?

(2) All analytic proper additive subgroups of R are meager. As a
consequence there is no proper additive subgroup of R which is G-
delta.

Question: What about higher G levels?

(3) Given an additive subgroup G of R there exists a unique additive
subgroup H of R such that G + H = R and G intersection H = {0}.

(4) If G and H are two analytic additive subgroups of R such that G +
H = R and G intersection H = {0} then G = R and H = {0} or vice versa.

Question: If G is analytic and non trivial ( != R or {0}) then H is
necessarily non analytic. If, further, G is countable (like Q or Z)
then H is not even measurable. What if G is uncountable? Is H
measurable in that case? Or does the answer depend on the specific G
we choose. What if G is the group in (1)?

(5) That measurable non analytic additive subgroups of R exist follows
easily by a cardinality argument. Is there a definable example?

Question: Is there an analytic additive subgroup of R which is not
Borel?

Guest

On Jul 13, 12:00 pm, tango <ashu1...@gmail.com> wrote:

Guest

On Jul 14, 1:19 pm, fjbl...@yahoo.com wrote: