---
title: "Die Vollständigkeit der Axiome des logischen Funktionenkalküls"
authors:
  - "Kurt Gödel"
year: 1930
venue: "Monatshefte für Mathematik und Physik"
arxiv: null
doi: "10.1007/BF01692469"
source: "https://doi.org/10.1007/BF01692469"
topics:
  - completeness
  - first-order-logic
  - godel
seed_rank: 499
seed_batch: "foundations-greats-2026-08-13"
reviewed: "2026-08-13"
pool: "maths-foundations"
relevance_score: 10
lineage: foundations-of-computing
cites:
  - title: "Grundzüge der theoretischen Logik"
    url: "https://link.springer.com/book/10.1007/978-3-642-86848-1"
    year: 1928
    doi: "10.1007/978-3-642-86848-1"
see:
  - "491-grundzuge-der-theoretischen-logik"
---

# Die Vollständigkeit der Axiome des logischen Funktionenkalküls

## One-sentence takeaway

Gödel's completeness theorem: every valid first-order sentence has a finite proof in the Hilbert–Ackermann calculus, so FOL validity and provability coincide.

## Why it matters here

Separates "logic is complete" from "arithmetic is incomplete"; Broadside epistemology cards need both theorems, in this order, from the same author.

## Key ideas

- Thesis 1929 / paper 1930 in *Monatshefte* (DOI 10.1007/BF01692469), answering the completeness question left open by *Grundzüge*.
- If a sentence is true in every model, a formal derivation exists; equivalently, a consistent set of sentences has a model.
- Completeness is about the *logical* calculus, not about the arithmetical axioms he will show incomplete a year later.
- English working text is usually van Heijenoort's *From Frege to Gödel* translation.

## Caveats

## Links

- DOI: [10.1007/BF01692469](https://doi.org/10.1007/BF01692469)