Partitions and Indivisibility Properties of Countable Dimensional Vector Spaces
C. Laflamme, L. Nguyen Van The, M. Pouzet, N. Sauer
TL;DR
This paper explores partition properties of countable-dimensional vector spaces and relational structures, providing examples and counterexamples to understand indivisibility and partition phenomena in infinite structures.
Contribution
It introduces new examples of relational structures with specific indivisibility properties and extends partition results to infinite-dimensional vector spaces.
Findings
Provided examples of age indivisible structures not weakly indivisible
Extended partition results to infinite-dimensional vector spaces
Presented counterexamples in relational structure partition problems
Abstract
We investigate infinite versions of vector and affine space partition results, and thus obtain examples and a counterexample for a partition problem for relational structures. In particular we provide two (related) examples of an age indivisible relational structure which is not weakly indivisible.
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Taxonomy
TopicsAdvanced Topology and Set Theory · Limits and Structures in Graph Theory · Finite Group Theory Research