Structures, Models, and Satisfaction

Serafim Batzoglou
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Chapter Chapter 4 in Introduction to Incompleteness, 2024, pp 55-64 from Springer

Abstract: Abstract To recap, an axiomatic system that can represent recursive functions entails arithmetic sentences σ $$\sigma $$ that are true and not provable in the system. The system cannot prove its own consistency, represented by ¬ Prov ( ⌈ ⊥ ⌉ ) $$\lnot \mathrm {Prov}(\lceil \bot \rceil )$$ , unless it is inconsistent.

Date: 2024
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DOI: 10.1007/978-3-031-64217-3_4

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