The Undecidable: Basic Papers on Undecidable Propositions, Unsolvable Problems and Computable FunctionsMartin Davis |
Contents
On Formally Undecidable Propositions of | 4 |
On Undecidable Propositions of Formal | 39 |
On Intuitionistic Arithmetic and Number Theory | 75 |
Copyright | |
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a₁ Alonzo Church arbitrary argument axioms C-K ordinal formula canonical form Church complete configuration computable function computable numbers concept consistency consistency proof constructive conv convertible corresponding decision problem defined definition determine effectively calculable Entscheidungsproblem enunciation equations equivalent exists expression finite number finite sequence footnote formal free variables given Gödel representation Hence induction infinite intuitive Kleene Kurt Gödel Lemma m-configuration Math mathematical means metamathematical method n-th natural numbers normal form normal system notes number-theoretic theorems obtained occur operations ordinal logic P₁ paper partial recursive positive integers premise primitive assertion primitive letters primitive recursive function Principia Mathematica production proof provable formulas prove quantifiers recursive relation recursively enumerable set reducibility replace result Rosser rules S₁ S₂ set of positive square subset substitution suppose symbolic logic tion Turing Turing's undecidable proposition valid w-consistent well-formed formulas