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On the Effectiveness of Partition Re...

Laboska, Gabriela,

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On the Effectiveness of Partition Regularity over Algebraic Structures /

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	On the Effectiveness of Partition Regularity over Algebraic Structures // Gabriela Laboska.
作者:	Laboska, Gabriela,
面頁冊數:	1 electronic resource (68 pages)
附註:	Source: Dissertations Abstracts International, Volume: 87-01, Section: B.
Contained By:	Dissertations Abstracts International87-01B.
標題:	Mathematics. -
電子資源:	https://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=31939360
ISBN:	9798286457243

On the Effectiveness of Partition Regularity over Algebraic Structures /
Laboska, Gabriela,

On the Effectiveness of Partition Regularity over Algebraic Structures /Gabriela Laboska. - 1 electronic resource (68 pages)

Source: Dissertations Abstracts International, Volume: 87-01, Section: B.

Partition regularity over algebraic structures is a topic in Ramsey theory that has been extensively researched by combinatorialists. Motivated by recent work in this area, we investigate the computability-theoretic and reverse-mathematical aspects of partition regularity over algebraic structures-an area that, to the best of our knowledge, has not been explored before. This thesis focuses on a 1975 theorem by Straus, which has played a significant role in many of the results in this field.We show that Straus' theorem does not hold computably, and we investigate different cases of the theorem. For the simplest case n=1, we show that the best possible computability-theoretic bound for this problem are the PA degrees. We show something similar for the case n>1, under one additional condition.Since the PA degrees already have implications for the reverse mathematics of the theorem, we show that several cases of the theorem are equivalent to WKL0 over RCA0, as well as the fact that WKL0 implies the full Straus' theorem over RCA0.

English

ISBN: 9798286457243Subjects--Topical Terms:

515831
Mathematics.
Subjects--Index Terms:

Computability theory

On the Effectiveness of Partition Regularity over Algebraic Structures /
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500 $a Advisors: Malliaris, Maryanthe; Hirschfeldt, Denis.
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520 $a Partition regularity over algebraic structures is a topic in Ramsey theory that has been extensively researched by combinatorialists. Motivated by recent work in this area, we investigate the computability-theoretic and reverse-mathematical aspects of partition regularity over algebraic structures-an area that, to the best of our knowledge, has not been explored before. This thesis focuses on a 1975 theorem by Straus, which has played a significant role in many of the results in this field.We show that Straus' theorem does not hold computably, and we investigate different cases of the theorem. For the simplest case n=1, we show that the best possible computability-theoretic bound for this problem are the PA degrees. We show something similar for the case n>1, under one additional condition.Since the PA degrees already have implications for the reverse mathematics of the theorem, we show that several cases of the theorem are equivalent to WKL0 over RCA0, as well as the fact that WKL0 implies the full Straus' theorem over RCA0.
546 $a English
590 $a School code: 0330
650 4 $a Mathematics. $3 515831
650 4 $a Theoretical mathematics. $3 3173530
653 $a Computability theory
653 $a Partition regularity
653 $a Reverse mathematics
690 $a 0405
690 $a 0642
710 2 $a The University of Chicago. $b Mathematics. $e degree granting institution. $3 3823067
720 1 $a Malliaris, Maryanthe $e degree supervisor.
720 1 $a Hirschfeldt, Denis $e degree supervisor.
773 0 $t Dissertations Abstracts International $g 87-01B.
790 $a 0330
791 $a Ph.D.
792 $a 2025
856 4 0 $u https://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=31939360