For propositional logic it can be decided whether a formula has a deduction from a finite set of other formulaas. This volume begins with a method to decide this for the quantified formulas of those fragments of arithmetic which express the properties of order-plus-successor and of order-plus-addition (Pressburger arithmetic). It makes use of an algorithm eliminating quantifiers which, in turn, is also applied to obtain consistency proofs for these fragments.
For propositional logic it can be decided whether a formula has a deduction from a finite set of other formulaas. This volume begins with a method to decide this for the quantified formulas of those fragments of arithmetic which express the properties of order-plus-successor and of order-plus-addition (Pressburger arithmetic). It makes use of an algorithm eliminating quantifiers which, in turn, is also applied to obtain consistency proofs for these fragments.
1. Consistency Decidability Completeness for the Arithmetic of Order with Successor 2. Consistency Decidability Completeness for the Arithmetic of Addition and Order 3. Antinomies Pseudomenos and Their Analysis 4. Undefinability and Incompleteness General Theory 5.Elementary and Primitive Recursive Functions 6. Recursive Relations and Recursive Functions 7. The Arithmitization of Syntax 8. Consequences of Arithmetization 9. Axioms for Arithmetic 10. Peano Arithmetic PA and Its Expansion PR 11. Unprovability of Consistency
1. Consistency Decidability Completeness for the Arithmetic of Order with Successor 2. Consistency Decidability Completeness for the Arithmetic of Addition and Order 3. Antinomies Pseudomenos and Their Analysis 4. Undefinability and Incompleteness General Theory 5.Elementary and Primitive Recursive Functions 6. Recursive Relations and Recursive Functions 7. The Arithmitization of Syntax 8. Consequences of Arithmetization 9. Axioms for Arithmetic 10. Peano Arithmetic PA and Its Expansion PR 11. Unprovability of Consistency
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