dorsal/arxiv
View SchemaA Quantum Gate as a Physical Model of an Universal Arithmetical Algorithm without Church's Undecidability and Godel's Incompleteness
| Authors | Vladan Pankovic, Milan Predojevic |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0602009 |
| URL | https://arxiv.org/abs/quant-ph/0602009 |
Abstract
In this work we define an universal arithmetical algorithm, by means of the standard quantum mechanical formalism, called universal qm-arithmetical algorithm. By universal qm-arithmetical algorithm any decidable arithmetical formula (operation) can be decided (realized, calculated. Arithmetic defined by universal qm-arithmetical algorithm called qm-arithmetic one-to-one corresponds to decidable part of the usual arithmetic. We prove that in the qm-arithmetic the undecidable arithmetical formulas (operations) cannot exist (cannot be consistently defined). Or, we prove that qm-arithmetic has no undecidable parts. In this way we show that qm-arithmetic, that holds neither Church's undecidability nor Godel's incompleteness, is decidable and complete. Finally, we suggest that problems of the foundation of the arithmetic, can be solved by qm-arithmetic.
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"abstract": "In this work we define an universal arithmetical algorithm, by means of the\nstandard quantum mechanical formalism, called universal qm-arithmetical\nalgorithm. By universal qm-arithmetical algorithm any decidable arithmetical\nformula (operation) can be decided (realized, calculated. Arithmetic defined by\nuniversal qm-arithmetical algorithm called qm-arithmetic one-to-one corresponds\nto decidable part of the usual arithmetic. We prove that in the qm-arithmetic\nthe undecidable arithmetical formulas (operations) cannot exist (cannot be\nconsistently defined). Or, we prove that qm-arithmetic has no undecidable\nparts. In this way we show that qm-arithmetic, that holds neither Church\u0027s\nundecidability nor Godel\u0027s incompleteness, is decidable and complete. Finally,\nwe suggest that problems of the foundation of the arithmetic, can be solved by\nqm-arithmetic.",
"arxiv_id": "quant-ph/0602009",
"authors": [
"Vladan Pankovic",
"Milan Predojevic"
],
"categories": [
"quant-ph"
],
"title": "A Quantum Gate as a Physical Model of an Universal Arithmetical Algorithm without Church\u0027s Undecidability and Godel\u0027s Incompleteness",
"url": "https://arxiv.org/abs/quant-ph/0602009"
},
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