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On the Effectiveness of Partition Regularity over Algebraic Structures
On the Effectiveness of Partition Regularity over Algebraic Structures
상세정보
- 자료유형
- 학위논문 서양
- 최종처리일시
- 20260202103129
- ISBN
- 9798286457243
- DDC
- 510
- 서명/저자
- On the Effectiveness of Partition Regularity over Algebraic Structures
- 발행사항
- [Sl] : The University of Chicago, 2025
- 발행사항
- Ann Arbor : ProQuest Dissertations & Theses, 2025
- 형태사항
- 68 p
- 주기사항
- Source: Dissertations Abstracts International, Volume: 87-01, Section: B.
- 주기사항
- Advisor: Malliaris, Maryanthe;Hirschfeldt, Denis.
- 학위논문주기
- Thesis (Ph.D.)--The University of Chicago, 2025.
- 초록/해제
- 요약Partition 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 n1, 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.
- 일반주제명
- Mathematics
- 일반주제명
- Theoretical mathematics
- 기타저자
- The University of Chicago Mathematics
- 기본자료저록
- Dissertations Abstracts International. 87-01B.
- 전자적 위치 및 접속
- 로그인 후 원문을 볼 수 있습니다.
MARC
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■020 ▼a9798286457243
■035 ▼a(MiAaPQ)AAI31939360
■040 ▼aMiAaPQ▼cMiAaPQ
■0820 ▼a510
■1001 ▼aLaboska, Gabriela.▼0(orcid)0000-0002-3080-3838
■24510▼aOn the Effectiveness of Partition Regularity over Algebraic Structures
■260 ▼a[Sl]▼bThe University of Chicago▼c2025
■260 1▼aAnn Arbor▼bProQuest Dissertations & Theses▼c2025
■300 ▼a68 p
■500 ▼aSource: Dissertations Abstracts International, Volume: 87-01, Section: B.
■500 ▼aAdvisor: Malliaris, Maryanthe;Hirschfeldt, Denis.
■5021 ▼aThesis (Ph.D.)--The University of Chicago, 2025.
■520 ▼aPartition 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 n1, 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.
■590 ▼aSchool code: 0330.
■650 4▼aMathematics
■650 4▼aTheoretical mathematics
■653 ▼aComputability theory
■653 ▼aPartition regularity
■653 ▼aReverse mathematics
■690 ▼a0405
■690 ▼a0642
■71020▼aThe University of Chicago▼bMathematics.
■7730 ▼tDissertations Abstracts International▼g87-01B.
■790 ▼a0330
■791 ▼aPh.D.
■792 ▼a2025
■793 ▼aEnglish
■85640▼uhttp://www.riss.kr/pdu/ddodLink.do?id=T17357091▼nKERIS▼z이 자료의 원문은 한국교육학술정보원에서 제공합니다.
