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R. Kaye (1991)
Models of Peano arithmetic, 15
C. Freiling (1986)
Axioms of symmetry: Throwing darts at the real number lineJournal of Symbolic Logic, 51
Galen Weitkamp (1989)
The Sigma12 Theory of Axioms of SymmetryJ. Symb. Log., 54
(1993)
Model Theory, Encyclopedia of Mathematics and its Applications
A. Tzouvaras (1991)
A Note on Real Subsets of A Recursively Saturated ModelMath. Log. Q., 37
A. Tzouvaras (1992)
On expandability of models of Peano arithmetic to models of the alternative set theoryJournal of Symbolic Logic, 57
Galen Weitkamp (1989)
The Σ21 theory of axioms of symmetryJournal of Symbolic Logic, 54
C. Henson, Matt Kaufmann, H. Keisler (1984)
The strength of nonstandard methods in arithmeticJournal of Symbolic Logic, 49
We formulate C. Freiling's axioms of symmetry for general second-order structures with respect to a certain ideal of small sets contained in them and find several equivalent formulations of the principles. Then we focus on particular models, namely saturated and recursively saturated ones, and show that they are symmetric with respect to appropriate classes of small sets when their second-order part consists of definable sets. Some asymmetric models are also exhibited as well as partial asymmetric ones constructed by forcing.
Archive for Mathematical Logic – Springer Journals
Published: Feb 1, 2001
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