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On the theory of ∏_3^1 sets of reals

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.

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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).

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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.
Funding AgencyGrant Number
NSFMCS 76-17254
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Other Numbering System NameOther Numbering System ID
MathSciNet ReviewMR0465867
Issue or Number:1
Classification Code:AMS (MOS) subject classifications 1970: Primary 04A15, 02K30, 28A05, 54H05; Secondary 02F35, 02K25, 02K35, 04A30
Record Number:CaltechAUTHORS:20130625-140857081
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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
Deposited By: Ruth Sustaita
Deposited On:25 Jun 2013 22:55
Last Modified:09 Nov 2021 23:42

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