### Abstract

We validate an abstract formulation of Gödel's First and Second Incompleteness Theorems from a separate AFP entry by instantiating them to the case of finite sound extensions of the Hereditarily Finite (HF) Set theory, i.e., FOL theories extending the HF Set theory with a finite set of axioms that are sound in the standard model. The concrete results had been previously formalised in an AFP entry by Larry Paulson; our instantiation reuses the infrastructure developed in that entry.

### License

BSD License

### Topics

- Logic/Proof theory

### Session Goedel_HFSet_Semantic

- Instance

### Depends on

- An Abstract Formalization of Gödel’s Incompleteness Theorems
- Gödel’s Incompleteness Theorems

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## Cite

×

Goedel_HFSet_Semantic-AFP

    @article{Goedel_HFSet_Semantic-AFP,
      author  = {Andrei Popescu and Dmitriy Traytel},
      title   = {From Abstract to Concrete Gödel's Incompleteness Theorems—Part I},
      journal = {Archive of Formal Proofs},
      month   = {September},
      year    = {2020},
      note    = {\url{https://isa-afp.org/entries/Goedel_HFSet_Semantic.html},
                 Formal proof development},
      ISSN    = {2150-914x},
    }

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