Nonstandard Models of Arithmetic and Set Theory: AMS Special Session Nonstandard Models of Arithmetic and Set Theory, January 15-16, 2003, Baltimore, Maryland
American Mathematical Soc., 2004 - 167
This is the proceedings of the AMS special session on nonstandard models of arithmetic and set theory held at the Joint Mathematics Meetings in Baltimore (MD). The volume opens with an essay from Haim Gaifman that probes the concept of non-standardness in mathematics and provides a fascinating mix of historical and philosophical insights into the nature of nonstandard mathematical structures. In particular, Gaifman compares and contrasts the discovery of nonstandard models with other key mathematical innovations, such as the introduction of various number systems, the modern concept of function, and non-Euclidean geometries. Other articles in the book present results related to nonstandard models in arithmetic and set theory, including a survey of known results on the Turing upper bounds of arithmetic sets and functions. The volume is suitable for graduate students and research mathematicians interested in logic, especially model theory.
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Coding in IΔ0
Automorphisms Mahlo Cardinals and NFU
AC Fails in the Natural Analogues of V and L that Model the Stratified Fragment of ZF
Working with Nonstandard Models
Internally Iterated Ultrapowers
On Some Questions of Hrbacek and Di Nasso
Turing Upper Bounds of Jump Ideals and Scott Sets
Diversity in Substructures
Automorphisms of Countable Recursively Saturated Models of Set Theory
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a e Pº algebra arithmetical sets automorphism axioms Borel coding set cofinal computes an enumeration consistent construction Corollary countable jump ideal defined definition e-formula element elementary embedding elementary submodel elementary substructure equivalenced lattice exists extension family of sets finite formula FRIST Hence holds II(A induction infinite initial segment interpretation isomorphism iterated ultrapowers Lemma Logic Lt(M Mahlo cardinals Math Mathematics measurable cardinal model of IAo models of arithmetic models of set n e w n-symmetric natural numbers NFUA non-Euclidean geometry non-standard models nonstandard universe Ord is weakly ordinal parallel postulate partition Peano arithmetic permutations predicate proof of Theorem Proposition prove Rep(T satisfies saturated models Scott set sentences sequence Skolem Solovay standard model stratified structure subalgebras subsets Theorem 2.1 ultrafilter ultrapowers vo/P VP F weakly compact WSOL