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Prenex normalization and the hierarchical classification of formulas.
- Source :
-
Archive for Mathematical Logic . May2024, Vol. 63 Issue 3/4, p391-403. 13p. - Publication Year :
- 2024
-
Abstract
- Akama et al. [1] introduced a hierarchical classification of first-order formulas for a hierarchical prenex normal form theorem in semi-classical arithmetic. In this paper, we give a justification for the hierarchical classification in a general context of first-order theories. To this end, we first formalize the standard transformation procedure for prenex normalization. Then we show that the classes E k and U k introduced in [1] are exactly the classes induced by Σ k and Π k respectively via the transformation procedure in any first-order theory. [ABSTRACT FROM AUTHOR]
- Subjects :
- *CLASSIFICATION
*ARITHMETIC
Subjects
Details
- Language :
- English
- ISSN :
- 09335846
- Volume :
- 63
- Issue :
- 3/4
- Database :
- Academic Search Index
- Journal :
- Archive for Mathematical Logic
- Publication Type :
- Academic Journal
- Accession number :
- 176498197
- Full Text :
- https://doi.org/10.1007/s00153-023-00899-x