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The self-embedding theorem of WKL0 and a non-standard method
Annals of Pure and Applied Logic 84 (1):41-49 (1997)
Abstract
We prove that every countable non-standard model of WKL0 has a proper initial part isomorphic to itself. This theorem enables us to carry out non-standard arguments over WKL0.Other Versions
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Citations of this work
Nonstandard arithmetic and reverse mathematics.H. Jerome Keisler - 2006 - Bulletin of Symbolic Logic 12 (1):100-125.
Unifying the model theory of first-order and second-order arithmetic via WKL 0 ⁎.Ali Enayat & Tin Lok Wong - 2017 - Annals of Pure and Applied Logic 168 (6):1247-1283.
A Nonstandard Counterpart of WWKL.Stephen G. Simpson & Keita Yokoyama - 2011 - Notre Dame Journal of Formal Logic 52 (3):229-243.
Categorical characterizations of the natural numbers require primitive recursion.Leszek Aleksander Kołodziejczyk & Keita Yokoyama - 2015 - Annals of Pure and Applied Logic 166 (2):219-231.
Weaker cousins of Ramsey's theorem over a weak base theory.Marta Fiori-Carones, Leszek Aleksander Kołodziejczyk & Katarzyna W. Kowalik - 2021 - Annals of Pure and Applied Logic 172 (10):103028.
References found in this work
Countable models of set theories.Harvey Friedman - 1973 - In A. R. D. Mathias & Hartley Rogers (eds.), Cambridge Summer School in Mathematical Logic. New York,: Springer Verlag. pp. 539--573.
Initial Segments of Models of Peano's Axioms.L. A. S. Kirby, J. B. Paris, A. Lachlan, M. Srebrny & A. Zarach - 1983 - Journal of Symbolic Logic 48 (2):482-483.
A Note on a Theorem of H. FRIEDMAN.C. Dimitracopoulos & J. Paris - 1988 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 34 (1):13-17.
A Generalization of a Theorem of H. Friedman.C. Dimitracopoulos - 1985 - Mathematical Logic Quarterly 31 (14-18):221-225.
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