Contents Preface Introduction §1. On effective descriptive set theory 1.1. Spaces and sets 1.2. The classical hierarchies 1.3. Enumeration of bases 1.4. The effective hierarchy 1.5. Relationships between the classes 1.6. Uniformization, reduction, and separation 1.7. Enumeration of the classes 
§2. Topologies generated by effectively Suslin sets 2.1. Topology 2.2. Ensuring the non-emptiness of intersections 2.3. Some corollaries 2.4. Choquet spaces §3. First application: co-Suslin equivalence relations §4. Classification of Borel equivalence relations 4.1. Smooth relations 4.2. Glimm-Effros dichotomy 4.3. The case of closed relations 4.4. The case of non-closed relations 4.5. Embedding of E0 into E 4.6. Construction of the splitting system 4.7. Some other results §5. Decomposition of plane Borel sets 5.1. Decomposition theorem 5.2. Coding of Borel sets 5.3. Effective version of the Louveau theorem 5.4. Proof of the effective theorem 5.5. Concluding remark
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