Related Experiment Video
Updated: Aug 3, 2025

Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach
Published on: July 3, 2020
Some independence results related to finite trees
Harvey M Friedman1, Andreas Weiermann2
1Department of Mathematics, Ohio State University, Mathematics Building, 231 West 18th Avenue, Columbus, OH 43210, USA.
Abstract:
We investigate some concrete independence results for systems of reverse mathematics which emerge from monotonicity properties of number-theoretic functions. Natural properties of the less than or equal to relation with respect to sums of natural numbers lead to independence results for first-order Peano arithmetic. Natural properties of the less than or equal to relation with respect to sums and products of natural numbers lead to independence results for arithmetical transfinite recursion. By considering number-theoretic functions of arbitrary arities, we obtain independence results for systems beyond arithmetical transfinite recursion. We discuss how these embeddability relations are related to tree embeddability relations and we consider variants where the tree embeddability relation is not assumed to preserve infima. The findings of this paper are complementary to results on Kruskal-like theorems proved earlier by the first author. This article is part of the theme issue 'Modern perspectives in Proof Theory'.
Related Concept Videos
Introduction to Test of Independence
The test statistic for a test of independence is similar to that of a goodness-of-fit test:
Survival Tree
Building a Survival Tree
Constructing a...
Hypothesis Test for Test of Independence
H0: The two variables (factors)...
Phylogenetic Trees
Independent and Dependent Sources
Independent voltage or current sources supply a fixed amount of voltage or current, respectively, which is unaffected by other elements within the circuit. These are represented using specific symbols. Independent voltage sources are symbolized with polarities (+ and -), indicating the direction of the...
Law of Independent Assortment

