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Related Experiment Video

Updated: Jun 2, 2026

Evaluating Dryocosmus Kuriphilus-induced Damage on Castanea Sativa

Evaluating Dryocosmus Kuriphilus-induced Damage on Castanea Sativa

Published on: August 30, 2018

Diamond on Kurepa trees.

Ziemowit Kostana¹, Assaf Rinot², Saharon Shelah^3,4

¹Institute of Mathematics of the Czech Academy of Sciences, Prague, Czech Republic.

Monatshefte Fur Mathematik

|June 1, 2026

Summary

This summary is machine-generated.

Researchers introduced a weaker diamond variation for Kurepa trees. This principle is compatible with Martin's axiom but can consistently fail, proving its non-triviality.

Keywords:

Diamond Forcing with side conditions Kurepa hypothesis Weak Kurepa tree

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Last Updated: Jun 2, 2026

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Area of Science:

Set Theory
Combinatorial Mathematics

Background:

The diamond principle is a significant concept in set theory, used to study the structure of trees.
Investigating weaker variations of combinatorial principles can reveal new insights into the consistency and independence of mathematical statements.

Purpose of the Study:

To introduce and analyze a new, weaker variation of the diamond principle.
To explore the relationship between this new principle and Martin's axiom.
To determine the consistency strength and potential for failure of this weaker principle.

Main Methods:

Defining a new weak variation of the diamond principle tailored for Kurepa trees.
Proving the compatibility of this new principle with Martin's axiom using forcing techniques.
Demonstrating the non-triviality of the principle by constructing models where it consistently fails.

Main Results:

The introduced weak diamond variation is significantly weaker than the standard diamond principle.
This weaker principle is consistent with Martin's axiom.
Models of set theory can be constructed where this principle fails, indicating it is not universally true.

Conclusions:

The new weak diamond variation provides a more nuanced tool for studying Kurepa trees.
The compatibility with Martin's axiom and the possibility of failure highlight the independence of this principle within set theory.