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Preliminaries

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Abstract

This section sets out the necessary mathematical preliminaries for the text. Generally speaking, familiarity is assumed with the development of set theory through the basics about the constructible hierarchy L and the method of forcing, and with the basic concepts and constructions of model theory. Nevertheless, in taking a historical approach well-known concepts are often formulated anew, their basic facts reviewed, and references provided as part of the development. In particular, a discussion of the forcing formalism is deferred until results achieved by that method are dealt with squarely. In what follows, some basic terminology and concepts are affirmed whose contextual review would break the pace of exposition, and some standing conventions established.

Keywords

  • Direct Limit
  • Predicate Symbol
  • Satisfaction Relation
  • Elementary Substructure
  • Elementary Embedding

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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© 2009 Springer-Verlag Berlin Heidelberg

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(2009). Preliminaries. In: The Higher Infinite. Springer Monographs in Mathematics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-88867-3_1

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  • DOI: https://doi.org/10.1007/978-3-540-88867-3_1

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-88866-6

  • Online ISBN: 978-3-540-88867-3

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