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- Syntax and semantics of the propositional and predicate calculus,completeness of Gentzen proof systems,formal theories,nonstandard models,Godel Incompleteness Theorems,Recursive and primitive recursive functions
- Church’s thesis,recursively enumerable setsCardinality,Enumerability,Diagonalization,Computability,First-Order Logic ,Uncomputability and Undecidability,Completeness, Compactness and Lowenheim-Skolem,Formal Arithmetic
- Diagonal Lemma, Godel and Tarski Theorems,Provability Predicates and Lob's Theorem,Computational ComplexityEffective computation,Register machines,Turing machines,Proof of their equivalence,Church's thesis,Elementary recursion theory
- Gödel's incompleteness theorem ,Propositional logic,Predicate calculus,Proof systemsComputability turing machines,Church-turing thesis,Unsolvable problems,Completeness
- Incompleteness,Tarski semantics,Propositional calculus,First order theories,Undecidability,Resolution ,Horn clauses,Effective computability