## Journal of Symbolic Logic

### Local-global properties of positive primitive formulas in the theory of spaces of orderings

M. Marshall

#### Abstract

The paper deals with pp formulas in the language of reduced special groups, and the question of when the validity of a pp formula on each finite subspace of a space of orderings implies its global validity [18]. A large new class of pp formulas is introduced for which this is always the case, assuming the space of orderings in question has finite stability index. The paper also considers pp formulas of the special type b ∈ ∏i=1ⁿ D〈1,a_i〉. Formulas of this type with n=3 are the simplest sort of pp formula not covered by the result, and are also the source of the recent counterexamples in [9] and [19].

#### Article information

Source
J. Symbolic Logic, Volume 71, Issue 4 (2006), 1097-1107.

Dates
First available in Project Euclid: 20 November 2006

https://projecteuclid.org/euclid.jsl/1164060446

Digital Object Identifier
doi:10.2178/jsl/1164060446

Mathematical Reviews number (MathSciNet)
MR2275850

Zentralblatt MATH identifier
1129.12005

Subjects
Primary: Primary 12D15, Secondary 11E81

#### Citation

Marshall, M. Local-global properties of positive primitive formulas in the theory of spaces of orderings. J. Symbolic Logic 71 (2006), no. 4, 1097--1107. doi:10.2178/jsl/1164060446. https://projecteuclid.org/euclid.jsl/1164060446

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