All Questions
3
questions
2
votes
1
answer
105
views
Where is the copy of $\mathbb{N}$ in the constructible hierarchy relative to a real closed field?
Let $X$ be a real closed field. Let us define a constructible hierarchy relative to $X$ is defined as follows. (This is slightly nonstandard terminology.). Let $L_0(X)=X$. For any ordinal $\beta$, ...
3
votes
1
answer
1k
views
Undefinable Real Numbers
Disclamer: I'm sure my definition of "definable" may be different than the/a established mathematical one, I am more than interested in learning why/how this is so, but that is not my question
Part 1:...
5
votes
0
answers
138
views
Where is the first gap in the constructible hierarchy relative to a real closed field?
This is a follow-up to my question here. Let $X= (A,+,*)$ be a real closed field. Let us define a constructible hierarchy relative to $X$ as follows. Let $D_0(X)=A\cup A^2 \cup \{+,*\}$. For any ...