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Mike Shulman
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What is the relationship between the surreal numbers and non-standard analysis?

In particular, is there a transfer principle for surreal numbers they way there is for NSA?

A specific situation in which such a transfer principle would be useful arose in the thread Uniformizing the surcomplex unit circleUniformizing the surcomplex unit circle ; can the surjectivity of the map $t \mapsto e^{it}$ from the reals to the complex unit circle be transferred to the surreals? Presumably, one would need a definition of the map that was in some sense first-order; what sorts of definitions count as first-order? It is not clear to me how definitions involving the two-sided bracket operation can be fit into a first-order framework.

What is the relationship between the surreal numbers and non-standard analysis?

In particular, is there a transfer principle for surreal numbers they way there is for NSA?

A specific situation in which such a transfer principle would be useful arose in the thread Uniformizing the surcomplex unit circle ; can the surjectivity of the map $t \mapsto e^{it}$ from the reals to the complex unit circle be transferred to the surreals? Presumably, one would need a definition of the map that was in some sense first-order; what sorts of definitions count as first-order? It is not clear to me how definitions involving the two-sided bracket operation can be fit into a first-order framework.

What is the relationship between the surreal numbers and non-standard analysis?

In particular, is there a transfer principle for surreal numbers they way there is for NSA?

A specific situation in which such a transfer principle would be useful arose in the thread Uniformizing the surcomplex unit circle ; can the surjectivity of the map $t \mapsto e^{it}$ from the reals to the complex unit circle be transferred to the surreals? Presumably, one would need a definition of the map that was in some sense first-order; what sorts of definitions count as first-order? It is not clear to me how definitions involving the two-sided bracket operation can be fit into a first-order framework.

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James Propp
James Propp
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Surreal numbers vs. non-standard analysis

What is the relationship between the surreal numbers and non-standard analysis?

In particular, is there a transfer principle for surreal numbers they way there is for NSA?

A specific situation in which such a transfer principle would be useful arose in the thread Uniformizing the surcomplex unit circle ; can the surjectivity of the map $t \mapsto e^{it}$ from the reals to the complex unit circle be transferred to the surreals? Presumably, one would need a definition of the map that was in some sense first-order; what sorts of definitions count as first-order? It is not clear to me how definitions involving the two-sided bracket operation can be fit into a first-order framework.