A Proof of the Schröder-Bernstein Theorem in ACL2
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866915409095032832 |
|---|---|
| author | Jurgensen, Grant |
| author_facet | Jurgensen, Grant |
| contents | The Schröder-Bernstein theorem states that, for any two sets P and Q, if there exists an injection from P to Q and an injection from Q to P, then there must exist a bijection between the two sets. Classically, it follows that the ordering of the cardinal numbers is antisymmetric. We describe a formulation and verification of the Schröder-Bernstein theorem in ACL2 following a well-known proof, introducing a theory of chains to define a non-computable witness. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_19008 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Proof of the Schröder-Bernstein Theorem in ACL2 Jurgensen, Grant Logic in Computer Science F.4.1 The Schröder-Bernstein theorem states that, for any two sets P and Q, if there exists an injection from P to Q and an injection from Q to P, then there must exist a bijection between the two sets. Classically, it follows that the ordering of the cardinal numbers is antisymmetric. We describe a formulation and verification of the Schröder-Bernstein theorem in ACL2 following a well-known proof, introducing a theory of chains to define a non-computable witness. |
| title | A Proof of the Schröder-Bernstein Theorem in ACL2 |
| topic | Logic in Computer Science F.4.1 |
| url | https://arxiv.org/abs/2507.19008 |