Kechris, Alexander S. (1975) The Theory of Countable Analytical Sets. Transactions of the American Mathematical Society, 202 (2). pp. 259297. ISSN 00029947. http://resolver.caltech.edu/CaltechAUTHORS:20130522132343731

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Abstract
The purpose of this paper is the study of the structure of countable sets in the various levels of the analytical hierarchy of sets of reals. It is first shown that, assuming projective determinacy, there is for each odd n a largest countable ∏_n^1 set of reals, C_n (this is also true for n even, replacing ∏_n^1 by Σ_n^1 and has been established earlier by Solovay for n = 2 and by Moschovakis and the author for all even n > 2). The internal structure of the sets C_n is then investigated in detail, the point of departure being the fact that each C_n is a set of Δ_n^1degrees, wellordered under their usual partial ordering. Finally, a number of applications of the preceding theory is presented, covering a variety of topics such as specification of bases, ωmodels of analysis, higherlevel analogs of the constructible universe, inductive definability, etc.
Item Type:  Article  

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Additional Information:  © 1975 American Mathematical Society. Received by the editors September 13, 1973. Research partially supported by NSF grant GP 27964.  
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Classification Code:  AMS (MOS) subject classifications (1970). Primary 04A15, 02K30, 28A05, 54H05; Secondary 02F35, 02K05, 02K25, 02K35, 04A30.  
Record Number:  CaltechAUTHORS:20130522132343731  
Persistent URL:  http://resolver.caltech.edu/CaltechAUTHORS:20130522132343731  
Official Citation:  The theory of countable analytical sets Alexander S. Kechris. Trans. Amer. Math. Soc. 202 (1975), 259297  
Usage Policy:  No commercial reproduction, distribution, display or performance rights in this work are provided.  
ID Code:  38637  
Collection:  CaltechAUTHORS  
Deposited By:  Ruth Sustaita  
Deposited On:  22 May 2013 20:52  
Last Modified:  13 Feb 2019 18:05 
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