New answers tagged nonstandard-analysis
3
votes
Surreals and NSA: some foundational issues
Problem 1: There is a definable proper class saturated real-closed field $\mathbb{R}^*$, defined by a slight modification of your and Shelah's construction, such that there is an $\mathrm{OD}_p$ ...
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2
votes
Finitistic interpretation of Nelson's internal set theory
Building on work by Benno van den Berg et al, the quantifiers $(\forall^{st}x)$ and $(\exists^{st}x)$ can be interpreted as "for all computationally relevant objects $x$" and "there ...
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10
votes
Do the surreal numbers enjoy the transfer principle in ZFC?
A partial answer to the focused question: it's not provable in ZFC that there is an OD class $\mathbb{Z}^*$ such that $(\mathbb{R}, +, \cdot, \mathbb{Z}) \equiv (\mathrm{No}, +, \cdot, \mathbb{Z}^*).$ ...
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16
votes
Do the surreal numbers enjoy the transfer principle in ZFC?
In $\mathsf{ZFC}$ if any two proper class models of the theory of an infinite set are isomorphic, then global choice holds. This is because $V$ and $\mathrm{Ord}$ are both models of this theory and an ...
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0
votes
In hyperreal field, can ln(ε) and ln(ω) be expressed as infinite sums?
I will propose an answer my question. Please let me know if I have spoken accurately.
Within the hyperreal field (that is, the most traditional hyperreal field as described by some of the original ...
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8
votes
In hyperreal field, can ln(ε) and ln(ω) be expressed as infinite sums?
To help avoid any misunderstanding that may arise for readers of this question, let me say that when understood in the usual sense, there are no nontrivial convergent sequences or series at all in the ...
- 236k
3
votes
In hyperreal field, can ln(ε) and ln(ω) be expressed as infinite sums?
For positive $\epsilon$, the expression $\ln \epsilon$ will be equal to its power series at $x=1$ (in the $\delta, N$ sense).
To help avoid any misunderstanding that may arise for readers of this ...
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