3,054 reputation
829
bio website cwru.edu/artsci/phil/…
location Case Western Reserve University
age 62
visits member for 2 years
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Apr
10
awarded  Yearling
Mar
29
asked $n$th order arithmetic with predicates for orders
Mar
23
awarded  Necromancer
Mar
18
comment Is realness of number fields exponentially bounded?
@GerryMyerson Yes. But for integers ``very small even up to conjugacy'' cannot.
Mar
18
comment Is realness of number fields exponentially bounded?
@GerryMyerson Consult MR0485681 as cited in user's answer. The magnitude bound is given not for separate conjugates, separately, but on the maximal complex magnitude of any conjugate of a given algebraic number. You can see why this is natural?
Mar
17
comment Quoting mathreviews
It is a good student question. Not research mathematics.
Mar
17
comment Would a non-constructible set become constructible if we had oracles of arbitrarily high cardinality for the halting problems of ordinal computers?
Constructibility of sets is not about making decisions. You cannot turn a set constructible by using more information. You probably want to know about relative constructibility as described on Wikipedia.
Mar
17
comment Is realness of number fields exponentially bounded?
@GerryMyerson The question concerns complexity. For integers, including algebraic integers, complexity agrees with magnitude, and so Raghavan's magnitude bound also bounds complexity. For rationals and other non-integer algebraic numbers very small can be very complex.
Mar
17
comment Is realness of number fields exponentially bounded?
But I believe stufe have not got to do with (necessarily) integral summands, and so do not directly address the question of complexity.
Mar
16
accepted Is realness of number fields exponentially bounded?
Mar
16
comment Is realness of number fields exponentially bounded?
Indeed this answers the question asked.
Mar
16
revised Is realness of number fields exponentially bounded?
Clarified question.
Mar
16
comment Is realness of number fields exponentially bounded?
Can you put some complexity bound on the summands $x_1,x_2,x_3,x_4,x_5$ themselves? Or on your $a,b,c,d$?
Mar
16
asked Is realness of number fields exponentially bounded?
Mar
2
revised Is the Modularity Theorem (currently) effective?
Clarified an issue.
Mar
2
awarded  Nice Question
Mar
2
accepted Is the Modularity Theorem (currently) effective?
Mar
2
comment Is the Modularity Theorem (currently) effective?
Yes of course searching a finite list is effective. Do we have an effective way to create the finite list?
Mar
2
comment Is the Modularity Theorem (currently) effective?
Non-effectiveness is no obstacle to validity of the proof. But I wonder if current proofs are effective.
Mar
2
asked Is the Modularity Theorem (currently) effective?