Goedel Proof, Information Transfer and Thermodynamics

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F60461373%3A22340%2F15%3A43900692" target="_blank" >RIV/60461373:22340/15:43900692 - isvavai.cz</a>

Výsledek na webu

—

DOI - Digital Object Identifier

—

Jazyk výsledku

angličtina

Název v původním jazyce

Goedel Proof, Information Transfer and Thermodynamics

Popis výsledku v původním jazyce

The formula of an arithmetic theory based on Peano Arithmetics is a chain of symbols of its meta-language in which the theory is formulated such that it is both in convenience with the syntax of the meta-language and with the inferential rules of the theory. Syntactic rules constructing formulae of the theory (but not only !) are not its inferential rules. Although the meta-language syntax is defined recursively - by the recursive writing of mathematical-logical claims, only those recursively written meta-language&apos;s chains which formulate mathematical-logical claims about finite (precisely recursive) sets of individua of the theory, computable totally (thus recursive) and as always true are the formulae 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 further axioms than only those of Peano). Also the chains expressing methodological claims, even being written recursively (Goedel Undecidable Formula) are not parts of the theory and also they are not of the inferential system; the same is for 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 construction, the structure of which is visible clearly, we are setting 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.

Název v anglickém jazyce

Goedel Proof, Information Transfer and Thermodynamics

Popis výsledku anglicky

The formula of an arithmetic theory based on Peano Arithmetics is a chain of symbols of its meta-language in which the theory is formulated such that it is both in convenience with the syntax of the meta-language and with the inferential rules of the theory. Syntactic rules constructing formulae of the theory (but not only !) are not its inferential rules. Although the meta-language syntax is defined recursively - by the recursive writing of mathematical-logical claims, only those recursively written meta-language&apos;s chains which formulate mathematical-logical claims about finite (precisely recursive) sets of individua of the theory, computable totally (thus recursive) and as always true are the formulae 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 further axioms than only those of Peano). Also the chains expressing methodological claims, even being written recursively (Goedel Undecidable Formula) are not parts of the theory and also they are not of the inferential system; the same is for 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 construction, the structure of which is visible clearly, we are setting 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.

Druh

J_ost - Ostatní články v recenzovaných periodicích

CEP obor

—

OECD FORD obor

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

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2015

Kód důvěrnosti údajů

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

Název periodika

IIAS-Transactions on System Research and Cybernetics

ISSN

1609-8625

e-ISSN

—

Svazek periodika

1

Číslo periodika v rámci svazku

1

Stát vydavatele periodika

CA - Kanada

Počet stran výsledku

11

Strana od-do

48-58

Kód UT WoS článku

—

EID výsledku v databázi Scopus

—