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# Positive Bounded Formulas

Henson, C. Ward and Iovino, José and Kechris, Alexander S. and Odell, Edward (2003) Positive Bounded Formulas. In: Analysis and Logic. London Mathematical Society Lecture Note Series. No.262. Cambridge University Press , Cambridge, pp. 21-30. ISBN 9781107360006. https://resolver.caltech.edu/CaltechAUTHORS:20180817-104143887

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## Abstract

In this chapter we introduce the key ingredients of the logic for normed space structures that is described in this paper. These are the positive bounded formulas and the concept of approximate satisfaction of such formulas in normed space structures. Let L be a signature for a normed space structure ℳ based on (M^(s) ∣ s ∈ S). Recall that S has a distinguished element s = S_ℝ for which M^(s) = ℝ is the sort of real numbers. We begin considering ℳ from the model theoretic point of view, introducing a formal language based on L and a semantics according to which this language is interpreted in ℳ. In addition to the symbols of the signature L, we also need for each element s of the sort index set S, a countable set of symbols called the variables of sort s. We begin defining the formal language by introducing the set of terms of L, or L-terms. Each term is a finite string of symbols, each of which may be a variable or a function symbol of L, or one of the symbols (or, which are used for punctuation. In this many-sorted context, each term is associated with a unique sort which indicates its range. The formal definition is recursive. Definition. An L-term with range of sort s is a string which can be obtained by finitely many applications of the following rules of formation: If x is a variable of L of sort s, then x is a term with range of sort s. […]

Item Type:Book Section
Related URLs:
URLURL TypeDescription
https://doi.org/10.1017/cbo9781107360006.007DOIArticle
Series Name:London Mathematical Society Lecture Note Series
Issue or Number:262
DOI:10.1017/cbo9781107360006.007
Record Number:CaltechAUTHORS:20180817-104143887
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20180817-104143887
Official Citation:Henson, C., Iovino, J., Kechris, A., & Odell, E. (2003). Positive Bounded Formulas. In C. Finet & C. Michaux (Eds.), Analysis and Logic (London Mathematical Society Lecture Note Series, pp. 21-30). Cambridge: Cambridge University Press. doi:10.1017/CBO9781107360006.007
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:88904
Collection:CaltechAUTHORS
Deposited By: George Porter
Deposited On:20 Aug 2018 15:10