### Abstract

We present an abstract formalization of Gödel's incompleteness theorems. We analyze sufficient conditions for the theorems' applicability to a partially specified logic. Our abstract perspective enables a comparison between alternative approaches from the literature. These include Rosser's variation of the first theorem, Jeroslow's variation of the second theorem, and the Swierczkowski–Paulson semantics-based approach. This AFP entry is the main entry point to the results described in our CADE-27 paper A Formally Verified Abstract Account of Gödel's Incompleteness Theorems. As part of our abstract formalization's validation, we instantiate our locales twice in the separate AFP entries Goedel_HFSet_Semantic and Goedel_HFSet_Semanticless.

### License

BSD License

### Topics

- Logic/Proof theory

### Session Goedel_Incompleteness

- Deduction2
- Abstract_Encoding
- Abstract_Representability
- Diagonalization
- Derivability_Conditions
- Goedel_Formula
- Standard_Model_More
- Abstract_First_Goedel
- Rosser_Formula
- Abstract_First_Goedel_Rosser
- Abstract_Second_Goedel
- Abstract_Jeroslow_Encoding
- Jeroslow_Original
- Jeroslow_Simplified
- Loeb_Formula
- Loeb
- Tarski
- All_Abstract

### Depends on

- Syntax-Independent Logic Infrastructure

### Used by

- From Abstract to Concrete Gödel’s Incompleteness Theorems—Part I
- From Abstract to Concrete Gödel’s Incompleteness Theorems—Part II

### Auto-related entries

- A Verified Efficient Implementation of the Weighted Path Order
- The Hales–Jewett Theorem
- Irrational numbers from THE BOOK
- Compositional BD Security
- The Safely Composable DOM

## Cite

×

Goedel_Incompleteness-AFP

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

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