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The Combinatorics and Absoluteness of Definable Sets of Real Numbers

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자료유형	E-Book
개인저자	Norwood, Zach.
단체저자명	University of California, Los Angeles. Mathematics 0540.
서명/저자사항	The Combinatorics and Absoluteness of Definable Sets of Real Numbers.
발행사항	[S.l.] : University of California, Los Angeles., 2018
발행사항	Ann Arbor : ProQuest Dissertations & Theses, 2018
형태사항	88 p.
소장본 주기	School code: 0031.
ISBN	9780438021716
일반주기	Source: Dissertation Abstracts International, Volume: 79-10(E), Section: A. Adviser: Itay Neeman.
요약	This thesis divides naturally into two parts, each concerned with the extent to which the theory of L(R) can be changed by forcing.
요약	The first part focuses primarily on applying generic-absoluteness principles to show that definable sets of reals enjoy regularity properties. We begin, in the spirit of Mathias, by establishing a strong Ramsey property for sets of reals in the
요약	In Chapter 3 we stray from the main line of inquiry to briefly study a game-theoretic characterization of filters with the Baire Property.
요약	Neeman and Zapletal showed, assuming roughly the existence of a proper class of Woodin cardinals, that the boldface theory of L( R) cannot be changed by proper forcing. They call their result the Embedding Theorem, because they conclude that in
요약	Part I concludes with Chapter 5, a short list of open questions.
요약	In the second part of the thesis, we conduct a finer analysis of the Embedding Theorem and its consistency strength. Schindler found that the the Embedding Theorem is consistent relative to much weaker assumptions than the existence of Woodin ca
요약	The proof of Theorem 6.2 splits naturally into two arguments. In Chapter 7 we extend Kunen's method of coding reals into a specializing function to allow for trees with uncountable levels that may not belong to L. This culminates in Theorem 7.4
요약	We complete the argument in Chapter 8, where we show that if the Tree Reflection Principle holds in every alpha-closed extension, then "special character omitted is remarkable in L.
요약	In Chapter 9 we review Schindler's proof of generic absoluteness from a remarkable cardinal to show that the argument gives a level-by-level upper bound.
요약	Chapter 10 is devoted to partially reversing the level-by-level upper bound of Chapter 9. We are able to show that L(R)-absoluteness for lambda-linked posets implies that the interval [kappa V1 ,lambda] is Sigma21-remarkable in L.
일반주제명	Logic.
언어	영어
기본자료 저록	Dissertation Abstracts International79-10A(E). Dissertation Abstract International
대출바로가기	http://www.riss.kr/pdu/ddodLink.do?id=T14998973