Definition of Ultraproducts. Meaning of Ultraproducts. Synonyms of Ultraproducts

- numbers, are a special case of this. Some striking applications of ultraproducts include very elegant proofs of the compactness theorem and the completeness...
- hypothesis holds. Ultraproducts are used as a general technique for constructing models that realise certain types. An ultraproduct is obtained from the...
- ISBN 978-1-4612-6619-8. J.L. Bell & A.B. Slomson (1969). Models and Ultraproducts. North Holland Publishing Company. Chapter 5, Theorem 4.3, page 103...
- theorem mentioned above also follows from this and an isomorphism of the ultraproducts (in both cases over all primes p) ulimp Qp ≅ ulimp Fp((t)). In addition...
- polynomials Fundamental theorem of topos theory Fundamental theorem of ultraproducts Fundamental theorem of vector analysis Carl Friedrich Gauss referred...
- page 5. Bell, John Lane; Slomson, Alan B. (2006) [1969]. Models and Ultraproducts: An Introduction (reprint of 1974 ed.). Dover Publications. ISBN 0-486-44979-3...
- His Ph.D. advisor was Alfred Tarski at Berkeley; his dissertation is Ultraproducts and Elementary classes (1961). Following Abraham Robinson's work resolving...
- numbers. The ultraproduct models are uncountable. One way to see this is to construct an injection of the infinite product of N into the ultraproduct. However...
- refer to truth but not to provability. One of those proofs relies on ultraproducts hinging on the axiom of choice as follows: Proof: Fix a first-order...
- Barwise and Feferman, Springer 1985 pps. 645–715. Keisler, HJ (1967). "Ultraproducts which are not saturated". J. Symb. Log. 32 (1): 23–46. doi:10.2307/2271240...