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Information Transfer and Thermodynamics Point of View on Goedel Proof

The result's identifiers

  • Result code in IS VaVaI

    <a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F60461373%3A22340%2F18%3A43913131" target="_blank" >RIV/60461373:22340/18:43913131 - isvavai.cz</a>

  • Result on the web

    <a href="http://dx.doi.org/10.5772/intechopen.68809" target="_blank" >http://dx.doi.org/10.5772/intechopen.68809</a>

  • DOI - Digital Object Identifier

    <a href="http://dx.doi.org/10.5772/intechopen.68809" target="_blank" >10.5772/intechopen.68809</a>

Alternative languages

  • Result language

    angličtina

  • Original language name

    Information Transfer and Thermodynamics Point of View on Goedel Proof

  • Original language description

    Formula of an arithmetic theory based on Peano Arithmetics (including it) is a chain of symbols of its super-language (in which the theory is formulated). Such a chain is both in convenience with the syntax of the super-language and with the inferential rules of the theory (Modus Ponens, Generalization). Syntactic rules constructing formulas of the theory are not its inferential rules. Although the super-language syntax is defined recursively - by the recursive writing of mathematical-logical claims - only those recursively written super-language&apos;s chains which formulate mathematical-logical claims about finite sets of individua of the theory, computable totally (thus recursive) and always true are the formulas of the theory. Formulas of the theory are not those claims which are true as for the individua of the theory, but not inferable within the theory (Great Fermat&apos;s Theorem). They are provable but within another theory (with both Peano and further axioms). Also the chains expressing methodological claims, even being written recursively (Goedel Undecidable Formula) are not parts of the theory. The same applies to their negations. We show the Goedel substitution function is not the total one and thus is not recursive. It is not defined for the Goedel Undecidable Formula&apos;s construction. For this case, the structure of which is visible clearly, we are adding the zero value. This correction is based on information, thermodynamic and computing considerations, simplifies the Goedel original proof and is valid for the consistent arithmetic theories directly.

  • Czech name

  • Czech description

Classification

  • Type

    C - Chapter in a specialist book

  • CEP classification

  • OECD FORD branch

    10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)

Result continuities

  • Project

  • Continuities

    I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Others

  • Publication year

    2018

  • Confidentiality

    S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Data specific for result type

  • Book/collection name

    Ontology in Information Science

  • ISBN

    978-953-51-5354-2

  • Number of pages of the result

    22

  • Pages from-to

    279-300

  • Number of pages of the book

    310

  • Publisher name

    InTech

  • Place of publication

    Rijeka

  • UT code for WoS chapter