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A sequence of theories for arithmetic whose union is complete. (English) Zbl 0411.03053


MSC:

03F30 First-order arithmetic and fragments
03H15 Nonstandard models of arithmetic

Citations:

Zbl 0316.02037
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References:

[1] S. Feferman , Arithmetization of Metamathematics in a general setting , Fund. Mat. 49 ( 1960 ) pp. 35 - 92 . Article | MR 147397 | Zbl 0095.24301 · Zbl 0095.24301
[2] S. Feferman , Transfinite recursive pregressions of axiomatic theories , Joun., of Symb. Logic , 27 ( 1962 ) pp. 259 - 316 . MR 172792 | Zbl 0117.25402 · Zbl 0117.25402 · doi:10.2307/2964649
[3] R. Magari , Significato e verità nell’aritmetica peaniana , Ann. di Mat. Pura e Appl. , 4 ( 103 ) 1975 , pp. 343 - 368 . MR 373875 | Zbl 0316.02037 · Zbl 0316.02037 · doi:10.1007/BF02414160
[4] M.H. Löb , Solution of a problem of Leon Henkin , Journ. of Symb. Logic , 20 ( 1955 ) pp. 115 - 118 . MR 70596 | Zbl 0067.00202 · Zbl 0067.00202 · doi:10.2307/2266895
[5] H. Rogers , Jr. Theory of recursive functions and effective computability , Mc Graw Hill ; New York , 1967 . MR 224462 | Zbl 0183.01401 · Zbl 0183.01401
[6] C. Smorynski , Consistency and related metamathematical properties , Amsterdam Mathematisch Instituut, Rp. 75 - 02 .
[7] A. Ursini , On the set of meaningful sentences of arithmetic , to appear in Studia Logica . MR 515169 | Zbl 0404.03043 · Zbl 0404.03043 · doi:10.1007/BF02124725
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