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The schematic CERES method has yielded significant results in proof theory, particularly in the analysis of proof schemata and the extraction of Herbrand systems. However, several challenges remain unresolved, leaving promising investigations for further exploration. This chapter outlines current open problems and concrete plans for future development, with particular emphasis on the completeness of schematic CERES, applications to arithmetic systems, and the ongoing extension of the GAPT system.

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Open Problems and Future Research

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  • 发表日期：

    2026年

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  • Alexander Leitsch,
  • David Michael Cerna,
  • Anela Lolic

摘要

The schematic CERES method has yielded significant results in proof theory, particularly in the analysis of proof schemata and the extraction of Herbrand systems. However, several challenges remain unresolved, leaving promising investigations for further exploration. This chapter outlines current open problems and concrete plans for future development, with particular emphasis on the completeness of schematic CERES, applications to arithmetic systems, and the ongoing extension of the GAPT system.