Abstract
According to Gödel's completeness theorem, every consistent theory1 has a model whose domain is a set of natural numbers. The objects of the model corresponding to the predicate symbols of the theory are then predicates of natural numbers. Kleene [5] p. 398 showed that, if the theory is axiomatizable,2 then the model can be chosen so that these predicates are in both two-quantifier forms, i.e., they can be expressed in both the forms (x)(Ey)R and (Ex)(y)S with R and S recursive. An alternative proof has been given by Hasen jaeger [3].
Publisher
Cambridge University Press (CUP)
Reference14 articles.
1. On axiomatizdbility within a system;Craig;this Journal,1953
2. Eine Bemerkung zu Henkin's Beweis für die Vollständigkeit der Prädikatenkalküls der ersten Stufe;Hasenjaeger;this Journal,1953
3. A formula with no recursively enumerable model
Cited by
35 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献
1. Direct Construction of Scott Ideals;Lecture Notes in Computer Science;2023
2. Provability logic: models within models in Peano Arithmetic;Bollettino dell'Unione Matematica Italiana;2022-05-07
3. THE PREHISTORY OF THE SUBSYSTEMS OF SECOND-ORDER ARITHMETIC;The Review of Symbolic Logic;2017-02-20
4. choice classes;Mathematical Logic Quarterly;2016-12
5. Peano Arithmetic Models and Computability;Algebraic Computability and Enumeration Models;2016-02-25