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Computable Structure Theory of Continuous Logic.

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Computable Structure Theory of Continuous Logic./
作者:	Camrud, Caleb Matthew.
面頁冊數:	1 online resource (101 pages)
附註:	Source: Dissertations Abstracts International, Volume: 83-12, Section: B.
Contained By:	Dissertations Abstracts International83-12B.
標題:	Mathematics. -
電子資源:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=28965629click for full text (PQDT)
ISBN:	9798819395783

Computable Structure Theory of Continuous Logic.
Camrud, Caleb Matthew.

Computable Structure Theory of Continuous Logic. - 1 online resource (101 pages)

Source: Dissertations Abstracts International, Volume: 83-12, Section: B.

Thesis (Ph.D.)--Iowa State University, 2022.

Includes bibliographical references

This dissertation examines computable structure theory relative to continuous logic. Due to the continuous nature of the relevant structures and space of truth values, special care is required to translate and modify results given in classical computable structure theory to the continuous setting. Three primary results are proven: (1) a generalized effective completeness theorem for continuous logic and computable presentations, (2) the existence of numerals for hyperarithmetical real numbers coded by computable infinitary sentences, and (3) upper and lower bounds on the complexity of the various diagram levels of the finitary and infinitary theories of a computably presented metric structure. Also given are basic model-theoretic results, an explicit formulation of the computable infinitary formulas of continuous logic, propositions concerning infinitary connectives, and a novel combinatorial result which allows for the encoding of a quantifier via a series inequality.

Electronic reproduction.
Ann Arbor, Mich. :
ProQuest,
2023

Mode of access: World Wide Web

ISBN: 9798819395783Subjects--Topical Terms:

515831
Mathematics.
Subjects--Index Terms:

Computability theoryIndex Terms--Genre/Form:

542853
Electronic books.

Computable Structure Theory of Continuous Logic.
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500 $a Source: Dissertations Abstracts International, Volume: 83-12, Section: B.
500 $a Advisor: McNicholl, Timothy.
502 $a Thesis (Ph.D.)--Iowa State University, 2022.
504 $a Includes bibliographical references
520 $a This dissertation examines computable structure theory relative to continuous logic. Due to the continuous nature of the relevant structures and space of truth values, special care is required to translate and modify results given in classical computable structure theory to the continuous setting. Three primary results are proven: (1) a generalized effective completeness theorem for continuous logic and computable presentations, (2) the existence of numerals for hyperarithmetical real numbers coded by computable infinitary sentences, and (3) upper and lower bounds on the complexity of the various diagram levels of the finitary and infinitary theories of a computably presented metric structure. Also given are basic model-theoretic results, an explicit formulation of the computable infinitary formulas of continuous logic, propositions concerning infinitary connectives, and a novel combinatorial result which allows for the encoding of a quantifier via a series inequality.
533 $a Electronic reproduction. $b Ann Arbor, Mich. : $c ProQuest, $d 2023
538 $a Mode of access: World Wide Web
650 4 $a Mathematics. $3 515831
650 4 $a Logic. $3 529544
650 4 $a Computer science. $3 523869
653 $a Computability theory
653 $a Computable structure theory
653 $a Continuous logic
653 $a Fuzzy logic
653 $a Model theory
653 $a Real analysis
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