Gödel’s incompleteness theorem
In this section we show how the syntax of formal languages reduces in principle to arithmetic. We do this by identifying the symbols, expressions, and texts in a finite or countable alphabet A with certain natural numbers (i.e., by numbering them) in such a way that the syntactic operations (juxtaposition, substitution, etc.) are represented by recursive functions, and the syntactic relations (occurrence in an expression, “being a formula,” etc.) are represented by decidable or enumerable sets.
KeywordsPartial Function Recursive Function Atomic Formula Diophantine Equation Incompleteness Theorem
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