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Ideal Analytic Sets
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DOI：10.1002/malq.70012.png)
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Abstract
En 中文
The aim of this study is to give natural examples of Sigma(1)(1)-complete and Pi(1)(1)-complete sets.In the first part, we consider ideals on omega . We use a unified approach introduced in [4] to create reductions of the collection of ill-founded trees to the ideals, proving Sigma(1)(1)-completeness of the ideals. In the second part, we show the connection between this topic, families of trees and coding of sigma-ideals of Polish spaces. In particular, we use the unified approach to prove that sets of codes for closed Ramsey-null sets, for closed sigma-compact sets and for closed not strongly dominating sets are Pi(1)(1)-complete.
Keywords:
analytic set
analytic-complete set
Borel reduction
Borel set
Hindman ideal
ideal
perfect tree
Polish space
superperfect tree
tree
Journal
M
IF:
0.4
Papers:
10
Citations:
0