Kechris, A. S. and Martin, D. A. (1978) On the theory of ∏_3^1 sets of reals. Bulletin of the American Mathematical Society, 84 (1). pp. 149-151. ISSN 0273-0979. doi:10.1090/S0002-9904-1978-14447-4. https://resolver.caltech.edu/CaltechAUTHORS:20130625-140857081
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Abstract
Assuming that ∀x Є ω^ω (x^# exists), let u_ɑ be the ɑth uniform indiscernible (see [3] or [2] ). A canonical coding system for ordinals < u_ω can be defined by letting W0_ω = {w Є ω^ω: w = (n, x^#), for some n Є ω, x Є ω^ω} and for w = (n, x^#) є W0_ω, │w│ = Ƭ^L_n [x](u_l',... , u_k_n), where T_n is the nth term in a recursive enumeration of all terms in the language of ZF + V = L [x], x a constant, taking always ordinal values. Call a relation P(ξ x), where ~varies over u^ω and x over ω^ω, ∏^1_k if P^*(w, x)⇔ w Є W0_ω Λ P(│w│, x) is ∏^1_k. An ordinal ξ < u_ω is called Δ^1_k if it has a Δ^1_k notation i.e. ∃ w Є W0_ω (w Є Δ^1_k Λ │w│ = ξ).
Item Type: | Article | |||||||||
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Additional Information: | © 1978 American Mathematical Society. Communicated by Solomon Feferman, June 2, 1977. Research partially supported by NSF Grant MCS 76-17254. | |||||||||
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Issue or Number: | 1 | |||||||||
Classification Code: | AMS (MOS) subject classifications 1970: Primary 04A15, 02K30, 28A05, 54H05; Secondary 02F35, 02K25, 02K35, 04A30 | |||||||||
DOI: | 10.1090/S0002-9904-1978-14447-4 | |||||||||
Record Number: | CaltechAUTHORS:20130625-140857081 | |||||||||
Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:20130625-140857081 | |||||||||
Official Citation: | On the theory of ∏_3^1 sets of reals A. S. Kechris and D. A. Martin. Bull. Amer. Math. Soc. 84 (1978), 149-151 | |||||||||
Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | |||||||||
ID Code: | 39092 | |||||||||
Collection: | CaltechAUTHORS | |||||||||
Deposited By: | Ruth Sustaita | |||||||||
Deposited On: | 25 Jun 2013 22:55 | |||||||||
Last Modified: | 09 Nov 2021 23:42 |
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