| LDR | | 03276nmm uu200481 4500 |
| 001 | | 000000331858 |
| 005 | | 20240805165521 |
| 008 | | 181129s2018 |||||||||||||||||c||eng d |
| 020 | |
▼a 9780438021716 |
| 035 | |
▼a (MiAaPQ)AAI10827047 |
| 035 | |
▼a (MiAaPQ)ucla:16891 |
| 040 | |
▼a MiAaPQ
▼c MiAaPQ
▼d 248032 |
| 082 | 0 |
▼a 160 |
| 100 | 1 |
▼a Norwood, Zach. |
| 245 | 14 |
▼a The Combinatorics and Absoluteness of Definable Sets of Real Numbers. |
| 260 | |
▼a [S.l.] :
▼b University of California, Los Angeles.,
▼c 2018 |
| 260 | 1 |
▼a Ann Arbor :
▼b ProQuest Dissertations & Theses,
▼c 2018 |
| 300 | |
▼a 88 p. |
| 500 | |
▼a Source: Dissertation Abstracts International, Volume: 79-10(E), Section: A. |
| 500 | |
▼a Adviser: Itay Neeman. |
| 502 | 1 |
▼a Thesis (Ph.D.)--University of California, Los Angeles, 2018. |
| 520 | |
▼a This thesis divides naturally into two parts, each concerned with the extent to which the theory of L(R) can be changed by forcing. |
| 520 | |
▼a 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 |
| 520 | |
▼a In Chapter 3 we stray from the main line of inquiry to briefly study a game-theoretic characterization of filters with the Baire Property. |
| 520 | |
▼a 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 |
| 520 | |
▼a Part I concludes with Chapter 5, a short list of open questions. |
| 520 | |
▼a 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 |
| 520 | |
▼a 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 |
| 520 | |
▼a 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. |
| 520 | |
▼a 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. |
| 520 | |
▼a 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. |
| 590 | |
▼a School code: 0031. |
| 650 | 4 |
▼a Logic. |
| 690 | |
▼a 0395 |
| 710 | 20 |
▼a University of California, Los Angeles.
▼b Mathematics 0540. |
| 773 | 0 |
▼t Dissertation Abstracts International
▼g 79-10A(E). |
| 773 | |
▼t Dissertation Abstract International |
| 790 | |
▼a 0031 |
| 791 | |
▼a Ph.D. |
| 792 | |
▼a 2018 |
| 793 | |
▼a English |
| 856 | 40 |
▼u http://www.riss.kr/pdu/ddodLink.do?id=T14998973
▼n KERIS |
| 980 | |
▼a 201812
▼f 2019 |
| 990 | |
▼a 관리자 |