Gödel's first incompleteness theorem (1931) establishes which fact about any consistent, recursively enumerable theory that includes sufficient arithmetic?

Gödel's first incompleteness theorem (1931) establishes which fact about any consistent, recursively enumerable theory that includes sufficient arithmetic?

Options:

1. It must be decidable
2. It proves every true arithmetic sentence
3. It contains true sentences that it cannot prove
4. It can prove its own consistency

Correct answer: It contains true sentences that it cannot prove

Explanation: Gödel's 1931 theorem shows such a theory has true but unprovable sentences, e.g., a constructed statement asserting its own unprovability in Peano arithmetic.

Created 2026-03-10T18:53:52.974Z. Updated 2026-03-10T18:53:52.974Z.