I've read Gödel's explanation and others but my understanding is unclear. Answers to the followup questions below would help:
- does ω-consistency have any relevance to methods or ideas not connected with Gödel numbering?
- Can we say that modus ponens and other rules of inference are ω-consistent?
- is there some philosophical significance to ω-consistency (for example, does it connect the idea of consistency to properties of natural numbers)?
Please explain in simple terms, if possible.