| Time: | 12 - 1:30 p.m. |
| Room: |
Wean Hall 7220
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| Speaker: | Chris Miller Associate Professor Department of Mathematics Ohio State University |
| Title: |
Avoiding the projective hierarchy in expansions of the real field by sequences
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| Abstract: |
Consider an expansion of the field of real numbers by a set of
real numbers {a_k: k in N} where a_k goes monotonically to +\infty as k
goes to +\infty. We are interested in knowing when the expansion does not
define the set of all natural numbers N. I will discuss some known
results. For example, N is not definable if (log a_{k+1})/(log a_k)
goes to +\infty (joint work with Harvey Friedman). On the other hand, N is
definable if (log a_k)/k goes to 0 subject to some further regularity
conditions. What happens in between these two extremes is more subtle, and
only partially understood.
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| Organizer's note: | Lunch will be provided.
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