Intuitionistic logic and axiomatic theories

Brablec, Vladimír

Intuicionistické logika a axiomatické teorie

dc.contributor.advisor	Švejdar, Vítězslav
dc.creator	Brablec, Vladimír
dc.date.accessioned	2017-04-27T04:34:21Z
dc.date.available	2017-04-27T04:34:21Z
dc.date.issued	2010
dc.identifier.uri	http://hdl.handle.net/20.500.11956/34313
dc.description.abstract	Pr ace zkoum a vlastnosti n ekter ych element arn ch intuicionistick ych teori . Vybr any jsou n asleduj c teorie: teorie rovnosti, line arn ho uspo r ad an , hust eho line arn ho uspo r ad an , teorie n asledn ka, Robinsonova aritmetika a teorie s c t an racion aln ch c sel; nav c t em e r ka zdou z t echto teori formulujeme dv ema r uzn ymi zp usoby. Z vlastnost teori n as zaj maj p redev s m n asleduj c cty ri: spl yv an s klasickou verz teorie, saturovanost, platnost De Jonghovy v ety a rozhodnutelnost. Diplomov a pr ace vych az zejm ena z v ysledk u C. Smorynsk eho a D. de Jongha a sna z se je rozvinout. N ekter e v ysledky zn am e pro Heytingovu aritmetiku dokazuje i pro jin e teorie. D ale se pokou s odpov ed et nap r klad na to, jak y vliv m a z am ena axiomu teorie za jin y (klasicky ekvivalentn ) axiom nebo jak e vlastnosti by m ela m t dobr a intuicionistick a teorie.	cs_CZ
dc.description.abstract	This thesis explores some properties of elementary intuitionistic theories. We focus on the following theories: the theory of equality, linear order, dense linear order, the theory of a successor function, Robinson arithmetic and the theory of rational numbers with addition; moreover, we usually deal with two dierent formulations of the theories. As for the properties, our main interest is in the following four: coincidence with the classical version of a theory, saturation, De Jongh's theorem and decidability. The thesis draws especially from the results of C. Smorynski and D. de Jongh and tries to develop them. Some results known for Heyting arithmetic are proved for other theories. We also try to answer the question of what is the eect of replacing an axiom by a dierent (classically equivalent) axiom, or which properties a \good" intuitionistic theory should have.	en_US
dc.language	English	cs_CZ
dc.language.iso	en_US
dc.publisher	Univerzita Karlova, Filozofická fakulta	cs_CZ
dc.title	Intuitionistic logic and axiomatic theories	en_US
dc.type	diplomová práce	cs_CZ
dcterms.created	2010
dcterms.dateAccepted	2010-09-16
dc.description.department	Department of Logic	en_US
dc.description.department	Katedra logiky	cs_CZ
dc.description.faculty	Faculty of Arts	en_US
dc.description.faculty	Filozofická fakulta	cs_CZ
dc.identifier.repId	90806
dc.title.translated	Intuicionistické logika a axiomatické teorie	cs_CZ
dc.contributor.referee	Jeřábek, Emil
dc.identifier.aleph	001368431
thesis.degree.name	Mgr.
thesis.degree.level	magisterské	cs_CZ
thesis.degree.discipline	Logic	en_US
thesis.degree.discipline	Logika	cs_CZ
thesis.degree.program	Logic	en_US
thesis.degree.program	Logika	cs_CZ
uk.thesis.type	diplomová práce	cs_CZ
uk.taxonomy.organization-cs	Filozofická fakulta::Katedra logiky	cs_CZ
uk.taxonomy.organization-en	Faculty of Arts::Department of Logic	en_US
uk.faculty-name.cs	Filozofická fakulta	cs_CZ
uk.faculty-name.en	Faculty of Arts	en_US
uk.faculty-abbr.cs	FF	cs_CZ
uk.degree-discipline.cs	Logika	cs_CZ
uk.degree-discipline.en	Logic	en_US
uk.degree-program.cs	Logika	cs_CZ
uk.degree-program.en	Logic	en_US
thesis.grade.cs	Velmi dobře	cs_CZ
thesis.grade.en	Very good	en_US
uk.abstract.cs	Pr ace zkoum a vlastnosti n ekter ych element arn ch intuicionistick ych teori . Vybr any jsou n asleduj c teorie: teorie rovnosti, line arn ho uspo r ad an , hust eho line arn ho uspo r ad an , teorie n asledn ka, Robinsonova aritmetika a teorie s c t an racion aln ch c sel; nav c t em e r ka zdou z t echto teori formulujeme dv ema r uzn ymi zp usoby. Z vlastnost teori n as zaj maj p redev s m n asleduj c cty ri: spl yv an s klasickou verz teorie, saturovanost, platnost De Jonghovy v ety a rozhodnutelnost. Diplomov a pr ace vych az zejm ena z v ysledk u C. Smorynsk eho a D. de Jongha a sna z se je rozvinout. N ekter e v ysledky zn am e pro Heytingovu aritmetiku dokazuje i pro jin e teorie. D ale se pokou s odpov ed et nap r klad na to, jak y vliv m a z am ena axiomu teorie za jin y (klasicky ekvivalentn ) axiom nebo jak e vlastnosti by m ela m t dobr a intuicionistick a teorie.	cs_CZ
uk.abstract.en	This thesis explores some properties of elementary intuitionistic theories. We focus on the following theories: the theory of equality, linear order, dense linear order, the theory of a successor function, Robinson arithmetic and the theory of rational numbers with addition; moreover, we usually deal with two dierent formulations of the theories. As for the properties, our main interest is in the following four: coincidence with the classical version of a theory, saturation, De Jongh's theorem and decidability. The thesis draws especially from the results of C. Smorynski and D. de Jongh and tries to develop them. Some results known for Heyting arithmetic are proved for other theories. We also try to answer the question of what is the eect of replacing an axiom by a dierent (classically equivalent) axiom, or which properties a \good" intuitionistic theory should have.	en_US
uk.file-availability	V
uk.publication.place	Praha	cs_CZ
uk.grantor	Univerzita Karlova, Filozofická fakulta, Katedra logiky	cs_CZ
dc.identifier.lisID	990013684310106986