Non-Standard Analysis Approach

[bo198214]

I'm interested in considering the properties of tetration from the perspective of hyperreal algebra and Non-Standard analysis. I would also like to consider analyzing tetration in complex spaces using non-standard complex analysis. I believe there is a great deal of potential in using this approach because relationships are easier to see using the infinitesimal approach than they are using the classical analytic approach.

I dont think non-standard analysis helps here.
The problems lie on a different level.
And there is anyway no monograph about tetration yet.

But perhaps you can explain first why you see potential in that approach. One never knows