I have almost no knowledge on mathematical logic though I went through the basic undergraduate courses on algebra, analysis and topology. I would like to self-study mathematical logic that will cover the following topics. I would be grateful if someone can advice books and resources that I should access as a first course learner.
Introduction, propositions, truth table, negation, conjunction and disjunction. Implications, biconditional propositions, converse, contrapositive and inverse propositions and precedence of logical operators. General Notions : Formal language, object and meta language, general definition of a Formal Theory/Formal Logic.
Propositional Logic : Formal theory for propositional calculus, derivation, proof, theorem, deduction theorem, conjunctive and disjunctive normal forms, semantics, truth tables, tautology,. adequate set of connectives, applications to switching circuits, logical consequence,consistency, maximal consistency, Leindenbaum lemma, soundness and completeness theorems, algebraic semantics.
Predicate Logic : First order language, symbolizing ordinary sentences into first order formulae, free and bound variables, interpretation and satisfiability, models, logical validity, formal theory for predicate calculus, theorems and derivations, deduction theorem, equivalence theorem, replacement theorem, choice rule, Prenex normal form, soundness theorem, completeness theorem, compactness theorem, First Order Theory with equality, examples of First order Theories (groups, rings, fields etc.).
