19 citations · 101 across the 35 of their papers we have counts for
5 papers · 1 filter
Set-theoretic reflection is equivalent to induction over well-founded classes
Anton Freund
We show that induction over -definable well-founded classes is equivalent to the reflection principle which asserts that any true formula of first order set theory wi…
A note on ordinal exponentiation and derivatives of normal functions
Anton Freund
Michael Rathjen and the present author have shown that -bar induction is equivalent to (a suitable formalization of) the statement that every normal function has a derivativ…
Predicative collapsing principles
Anton Freund
We show that arithmetical transfinite recursion is equivalent to a suitable formalization of the following: For every ordinal there exists an ordinal such that $1+β\cdot(β+…
How strong are single fixed points of normal functions?
Anton Freund
In a recent paper by M. Rathjen and the present author it has been shown that the statement ``every normal function has a derivative'' is equivalent to -bar induction. The e…
Derivatives of normal functions in reverse mathematics
Anton Freund, Michael Rathjen
Consider a normal function on the ordinals (i. e. a function that is strictly increasing and continuous at limit stages). By enumerating the fixed points of we obtain a…