Model Theory of Algebra and Arithmetic pp 312-337 | Cite as
A hierarchy of cuts in models of arithmetic
Conference paper
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Abstract
In this paper we show that it is possible to classify most of the natural families of cuts considered to date in terms of a single hierarchy. This classification gives conservation and independence results for fragments of arithmetic.
Keywords
Initial Segment Winning Strategy Peano Arithmetic Satisfaction Relation Reflection Principle
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References
- [1]C. Dimitracopoulos, Doctorial thesis, Manchester. To appear.Google Scholar
- [2]J. Ketonen & R. Solovay, "Rapidly growing Ramsey functions", to appear.Google Scholar
- [3]L. Kirby, "Initial segments of models of arithmetic", Doctorial thesis, Manchester, 1977.Google Scholar
- [4]L. Kirby & J. Paris, "Initial segments of models of Peano’s axioms". Springer-Verlag lecture notes in mathematics, Vol. 619.Google Scholar
- [5]G. Mills, "Extensions of models of Peano arithmetic" Doctorial thesis, Berkeley, 1977.Google Scholar
- [6]J. Paris, "Some independence results for Peano arithmetic", J.S.L. 43 (1978), pp. 725–731.MathSciNetzbMATHGoogle Scholar
- [7]J. Paris & L. Harrington, "An incompleteness in Peano arithmetic". Handbook for Mathematical Logic, (ed. J. Barwise.), North Holland, 1976, pp.1133–1142.Google Scholar
- [8]J. Paris & L. Kirby, "Σn-collection schemas in arithmetic". Logic Colloquium ’77, North Holland 1978, pp.199–209.Google Scholar
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© Springer-Verlag 1980