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Introduction

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Part of the Lecture Notes in Mathematics book series (LNM,volume 1999)

Abstract

Unbeknownst to the majority of algebraists, ultraproducts have been around in model-theory for more than half a century, since their first appearance in a paper by Łoś ([65]), although the construction goes even further back, to work of Skolem in 1938 on non-standard models of Peano arithmetic. Through Kochen’s seminal paper [61] and his joint work [9] with Ax, ultraproducts also found their way into algebra. They did not leave a lasting impression on the algebraic community though, shunned perhaps because there were conceived as non-algebraic, belonging to the alien universe of set-theory and non-standard arithmetic, a universe in which most mathematicians did not, and still do not feel too comfortable.

Keywords

  • Commutative Algebra
  • Characteristic Zero
  • Uniform Bound
  • Peano Arithmetic
  • Minimal Prime Ideal

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Schoutens, H. (2010). Introduction. In: The Use of Ultraproducts in Commutative Algebra. Lecture Notes in Mathematics(), vol 1999. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-13368-8_1

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