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YCor
YCor
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On Asymptotic Classesasymptotic classes of Finite Structuresfinite structures

I have a question about the following paper.:

ONEOne-DIMENSIONAL ASYMPTOTIC CLASSES OF FINITE STRUCTURESdimensional asymptotic classes of finite structures

By:by Macpherson and Steinhorn

   https://www.ams.org/journals/tran/2008-360-01/S0002-9947-07-04382-6/S0002-9947-07-04382-6(link at Trans.pdf AMS website).

Let $\mathbf{K}$ be a one-dimensional asymptotic class of finite structures.

The phrase "every infinite ultraproduct" appear in this paper several times. For example Lemma 2.5. This phrase is vague for me. What does that mean? Does it mean that the ultraproduct of evey infinite subclass of $\mathbf{K}$? or it means the ultraproduct of all members of $\mathbf{K}$ under different ultrafilters?

On Asymptotic Classes of Finite Structures

I have a question about the following paper.

ONE-DIMENSIONAL ASYMPTOTIC CLASSES OF FINITE STRUCTURES

By: Macpherson and Steinhorn

 https://www.ams.org/journals/tran/2008-360-01/S0002-9947-07-04382-6/S0002-9947-07-04382-6.pdf

Let $\mathbf{K}$ be a one-dimensional asymptotic class of finite structures.

The phrase "every infinite ultraproduct" appear in this paper several times. For example Lemma 2.5. This phrase is vague for me. What does that mean? Does it mean that the ultraproduct of evey infinite subclass of $\mathbf{K}$? or it means the ultraproduct of all members of $\mathbf{K}$ under different ultrafilters?

On asymptotic classes of finite structures

I have a question about the following paper:

One-dimensional asymptotic classes of finite structures

by Macpherson and Steinhorn  (link at Trans. AMS website).

Let $\mathbf{K}$ be a one-dimensional asymptotic class of finite structures.

The phrase "every infinite ultraproduct" appear in this paper several times. For example Lemma 2.5. This phrase is vague for me. What does that mean? Does it mean that the ultraproduct of evey infinite subclass of $\mathbf{K}$? or it means the ultraproduct of all members of $\mathbf{K}$ under different ultrafilters?

Adding a link to the paper
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user44191
user44191
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I have a question about the following paper.

ONE-DIMENSIONAL ASYMPTOTIC CLASSES OF FINITE STRUCTURES

By: Macpherson and Steinhorn

https://www.ams.org/journals/tran/2008-360-01/S0002-9947-07-04382-6/S0002-9947-07-04382-6.pdf

Let $\mathbf{K}$ be a one-dimensional asymptotic class of finite structures.

The phrase "every infinite ultraproduct" appear in this paper several times. For example Lemma 2.5. This phrase is vague for me. What does that mean? Does it mean that the ultraproduct of evey infinite subclass of $\mathbf{K}$? or it means the ultraproduct of all members of $\mathbf{K}$ under different ultrafilters?

I have a question about the following paper.

ONE-DIMENSIONAL ASYMPTOTIC CLASSES OF FINITE STRUCTURES

By: Macpherson and Steinhorn

Let $\mathbf{K}$ be a one-dimensional asymptotic class of finite structures.

The phrase "every infinite ultraproduct" appear in this paper several times. For example Lemma 2.5. This phrase is vague for me. What does that mean? Does it mean that the ultraproduct of evey infinite subclass of $\mathbf{K}$? or it means the ultraproduct of all members of $\mathbf{K}$ under different ultrafilters?

I have a question about the following paper.

ONE-DIMENSIONAL ASYMPTOTIC CLASSES OF FINITE STRUCTURES

By: Macpherson and Steinhorn

https://www.ams.org/journals/tran/2008-360-01/S0002-9947-07-04382-6/S0002-9947-07-04382-6.pdf

Let $\mathbf{K}$ be a one-dimensional asymptotic class of finite structures.

The phrase "every infinite ultraproduct" appear in this paper several times. For example Lemma 2.5. This phrase is vague for me. What does that mean? Does it mean that the ultraproduct of evey infinite subclass of $\mathbf{K}$? or it means the ultraproduct of all members of $\mathbf{K}$ under different ultrafilters?

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Mark Smith
Mark Smith
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On Asymptotic Classes of Finite Structures

I have a question about the following paper.

ONE-DIMENSIONAL ASYMPTOTIC CLASSES OF FINITE STRUCTURES

By: Macpherson and Steinhorn

Let $\mathbf{K}$ be a one-dimensional asymptotic class of finite structures.

The phrase "every infinite ultraproduct" appear in this paper several times. For example Lemma 2.5. This phrase is vague for me. What does that mean? Does it mean that the ultraproduct of evey infinite subclass of $\mathbf{K}$? or it means the ultraproduct of all members of $\mathbf{K}$ under different ultrafilters?