On Q
| Autor: | Visser, A., OFR - Theoretical Philosophy, LS Logica en grondslagen v.d. wiskunde |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2017 |
| Předmět: |
Mathematics(all)
Arts and Humanities(all) Property (philosophy) Modulo 02 engineering and technology 01 natural sciences Measure (mathematics) Theoretical Computer Science 0202 electrical engineering electronic engineering information engineering PA Equivalence relation Interpretability comparison of theories 0101 mathematics Weak theories Mathematics Discrete mathematics [$$\mathsf{PA}^-$$PA Arithmetic 010102 general mathematics Sense (electronics) comparison of t Pairing 020201 artificial intelligence & image processing Geometry and Topology Software [$$\mathsf{PA}^-$$PA- Arithmetic comparison of t |
| Zdroj: | Soft Computing, 21(1), 39. Springer Verlag Soft Computing, 21. Springer Verlag |
| ISSN: | 1433-7479 1432-7643 |
| Popis: | In this paper we study the theory Q. We prove a basic result that says that, in a sense explained in the paper, Q can be split into two parts. We prove some consequences of this result. (i) Q is not a poly-pair theory. This means that, in a strong sense, pairing cannot be defined in Q. (ii) Q does not have the Pudlak Property. This means that there two interpretations of $$\mathsf{S}^1_2$$S21 in Q which do not have a definably isomorphic cut. (iii) Q is not sententially equivalent with $$\mathsf{PA}^-$$PA-. This tells us that we cannot do much better than mutual faithful interpretability as a measure of sameness of Q and $$\mathsf{PA}^-$$PA-. We briefly consider the idea of characterizing Q as the minimal-in-some-sense theory of some kind modulo some equivalence relation. We show that at least one possible road towards this aim is closed. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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