Initial segments and end-extensions of models of arithmetic

884 24 2170 5 3121 document 2170 Wong10PhD.pdf application/pdf 662b2da57ee61fb766ad5fe543a0300b MD5 632992 2011-07-19 16:24:58 http://etheses.bham.ac.uk//id/eprint/884/3/Wong10PhD.pdf 884 3 1 application/pdf application/pdf en public

Wong10PhD.pdf

http://eprints.org/relation/hasVolatileVersion http://etheses.bham.ac.uk/id/document/8079 http://eprints.org/relation/hasVersion http://etheses.bham.ac.uk/id/document/8079 http://eprints.org/relation/hassmallThumbnailVersion http://etheses.bham.ac.uk/id/document/8079 http://eprints.org/relation/hasVolatileVersion http://etheses.bham.ac.uk/id/document/8080 http://eprints.org/relation/hasVersion http://etheses.bham.ac.uk/id/document/8080 http://eprints.org/relation/haspreviewThumbnailVersion http://etheses.bham.ac.uk/id/document/8080 http://eprints.org/relation/hasVolatileVersion http://etheses.bham.ac.uk/id/document/8081 http://eprints.org/relation/hasVersion http://etheses.bham.ac.uk/id/document/8081 http://eprints.org/relation/hasIndexCodesVersion http://etheses.bham.ac.uk/id/document/8081 http://eprints.org/relation/hasVolatileVersion http://etheses.bham.ac.uk/id/document/13362 http://eprints.org/relation/haspreviewThumbnailVersion http://etheses.bham.ac.uk/id/document/13362 http://eprints.org/relation/hasVersion http://etheses.bham.ac.uk/id/document/13362 2171 7 3122 document 2171 Decl_IS_Wong10PhD.pdf application/pdf 25f6e2e1310d0fae468f9b995715891f MD5 30584 2011-07-19 16:24:58 http://etheses.bham.ac.uk//id/eprint/884/2/Decl_IS_Wong10PhD.pdf 884 2 4 application/pdf application/pdf en staffonly

Decl_IS_Wong10PhD.pdf

http://eprints.org/relation/hasVolatileVersion http://etheses.bham.ac.uk/id/document/8082 http://eprints.org/relation/hasVersion http://etheses.bham.ac.uk/id/document/8082 http://eprints.org/relation/hasIndexCodesVersion http://etheses.bham.ac.uk/id/document/8082 http://eprints.org/relation/hasVolatileVersion http://etheses.bham.ac.uk/id/document/8084 http://eprints.org/relation/hasVersion http://etheses.bham.ac.uk/id/document/8084 http://eprints.org/relation/hassmallThumbnailVersion http://etheses.bham.ac.uk/id/document/8084 http://eprints.org/relation/hasVolatileVersion http://etheses.bham.ac.uk/id/document/8085 http://eprints.org/relation/hasVersion http://etheses.bham.ac.uk/id/document/8085 http://eprints.org/relation/haspreviewThumbnailVersion http://etheses.bham.ac.uk/id/document/8085 http://eprints.org/relation/hasVolatileVersion http://etheses.bham.ac.uk/id/document/8086 http://eprints.org/relation/hasVersion http://etheses.bham.ac.uk/id/document/8086 http://eprints.org/relation/hasIndexCodesVersion http://etheses.bham.ac.uk/id/document/8086 http://eprints.org/relation/hasVolatileVersion http://etheses.bham.ac.uk/id/document/13363 http://eprints.org/relation/haspreviewThumbnailVersion http://etheses.bham.ac.uk/id/document/13363 http://eprints.org/relation/hasVersion http://etheses.bham.ac.uk/id/document/13363 8079 2 10443 document 8079 small.png image/png 37d30190fe261d7b9d6aea6ae2c50e5f MD5 4055 2011-07-19 21:50:36 http://etheses.bham.ac.uk//id/eprint/884/4/small.png 884 4 4 image/png thumbnail_small Thumbnail Documents conversion from application/pdf to thumbnail_small en public

small.png

http://eprints.org/relation/isVersionOf http://etheses.bham.ac.uk/id/document/2170 http://eprints.org/relation/isVolatileVersionOf http://etheses.bham.ac.uk/id/document/2170 http://eprints.org/relation/issmallThumbnailVersionOf http://etheses.bham.ac.uk/id/document/2170 8080 2 10444 document 8080 preview.jpg image/jpeg 912955c5cfc7b16234edb37db15593b9 MD5 12205 2011-07-19 21:50:39 http://etheses.bham.ac.uk//id/eprint/884/5/preview.jpg 884 5 5 image/jpeg image/jpeg Thumbnail Documents conversion from application/pdf to thumbnail_preview en public

preview.jpg

http://eprints.org/relation/isVersionOf http://etheses.bham.ac.uk/id/document/2170 http://eprints.org/relation/isVolatileVersionOf http://etheses.bham.ac.uk/id/document/2170 http://eprints.org/relation/ispreviewThumbnailVersionOf http://etheses.bham.ac.uk/id/document/2170 8081 2 10446 document 8081 indexcodes.txt text/plain 7e31a1e6c6879a2f94ec0bc25dc746ca MD5 17599 2011-07-19 21:50:42 http://etheses.bham.ac.uk//id/eprint/884/6/indexcodes.txt 884 6 6 text/plain indexcodes Generate index codes conversion from application/pdf to indexcodes en public

indexcodes.txt

http://eprints.org/relation/isVersionOf http://etheses.bham.ac.uk/id/document/2170 http://eprints.org/relation/isVolatileVersionOf http://etheses.bham.ac.uk/id/document/2170 http://eprints.org/relation/isIndexCodesVersionOf http://etheses.bham.ac.uk/id/document/2170 8084 2 10449 document 8084 small.png image/png 28d200f087ccc3a1fefcbb8cc945ef83 MD5 9468 2011-07-19 21:50:56 http://etheses.bham.ac.uk//id/eprint/884/7/small.png 884 7 7 image/png thumbnail_small Thumbnail Documents conversion from application/pdf to thumbnail_small en staffonly

small.png

http://eprints.org/relation/isVersionOf http://etheses.bham.ac.uk/id/document/2171 http://eprints.org/relation/isVolatileVersionOf http://etheses.bham.ac.uk/id/document/2171 http://eprints.org/relation/issmallThumbnailVersionOf http://etheses.bham.ac.uk/id/document/2171 8085 2 10450 document 8085 preview.jpg image/jpeg 5ea8eb73b498d95daf5e78f26e0ec343 MD5 37557 2011-07-19 21:50:57 http://etheses.bham.ac.uk//id/eprint/884/8/preview.jpg 884 8 8 image/jpeg image/jpeg Thumbnail Documents conversion from application/pdf to thumbnail_preview en staffonly

preview.jpg

http://eprints.org/relation/isVersionOf http://etheses.bham.ac.uk/id/document/2171 http://eprints.org/relation/isVolatileVersionOf http://etheses.bham.ac.uk/id/document/2171 http://eprints.org/relation/ispreviewThumbnailVersionOf http://etheses.bham.ac.uk/id/document/2171 8086 2 10451 document 8086 indexcodes.txt text/plain 8f317d58dee3f1c18257685b3a40f148 MD5 1506 2011-07-19 21:51:01 http://etheses.bham.ac.uk//id/eprint/884/9/indexcodes.txt 884 9 9 text/plain indexcodes Generate index codes conversion from application/pdf to indexcodes en staffonly

indexcodes.txt

http://eprints.org/relation/isVersionOf http://etheses.bham.ac.uk/id/document/2171 http://eprints.org/relation/isVolatileVersionOf http://etheses.bham.ac.uk/id/document/2171 http://eprints.org/relation/isIndexCodesVersionOf http://etheses.bham.ac.uk/id/document/2171 13362 2 19371 document 13362 preview.png image/png eac6caa5551944305f2c56102051d5e0 MD5 12590 2011-07-21 10:50:13 http://etheses.bham.ac.uk//id/eprint/884/10/preview.png 884 10 10 image/png image/png en public

preview.png

http://eprints.org/relation/isVolatileVersionOf http://etheses.bham.ac.uk/id/document/2170 http://eprints.org/relation/ispreviewThumbnailVersionOf http://etheses.bham.ac.uk/id/document/2170 http://eprints.org/relation/isVersionOf http://etheses.bham.ac.uk/id/document/2170 13363 2 19374 document 13363 preview.png image/png 3bc8d74d26000ed28e8c66127180f0cc MD5 37631 2011-07-21 10:50:14 http://etheses.bham.ac.uk//id/eprint/884/11/preview.png 884 11 11 image/png image/png en staffonly

preview.png

http://eprints.org/relation/isVolatileVersionOf http://etheses.bham.ac.uk/id/document/2171 http://eprints.org/relation/ispreviewThumbnailVersionOf http://etheses.bham.ac.uk/id/document/2171 http://eprints.org/relation/isVersionOf http://etheses.bham.ac.uk/id/document/2171 archive 4031 disk0/00/00/08/84 2010-08-04 11:22:01 2019-01-23 09:53:04 2011-07-19 16:24:58 thesis show 0 Wong Tin Lok Kaye Richard University of Birmingham Initial segments and end-extensions of models of arithmetic unpub QA 10col_ephy This thesis is organized into two independent parts. In the first part, we extend the recent work on generic cuts by Kaye and the author. The focus here is the properties of the pairs (M, I) where I is a generic cut of a model M. Amongst other results, we characterize the theory of such pairs, and prove that they are existentially closed in a natural category. In the second part, we construct end-extensions of models of arithmetic that are at least as strong as ATR\(_0\). Two new constructions are presented. The first one uses a variant of Fodor’s Lemma in ATR\(_0\) to build an internally rather classless model. The second one uses some weak versions of the Galvin–Prikry Theorem in adjoining an ideal set to a model of second-order arithmetic. 2010-07 2010-05 graduation eng author unchecked This unpublished thesis/dissertation is copyright of the author and/or third parties. The intellectual property rights of the author or third parties in respect of this work are as defined by The Copyright Designs and Patents Act 1988 or as modified by any successor legislation. Any use made of information contained in this thesis/dissertation must be in accordance with that legislation and must be properly acknowledged. Further distribution or reproduction in any format is prohibited without the permission of the copyright holder. Overseas Research Students Awards Scheme public 119 University of Birmingham School of Mathematics d_ph FALSE other 2010-07 graduation