## Abstract Two classically equivalent, but constructively inequivalent, strict convexity properties of a preference relation are discussed, and conditions given under which the stronger notion is a consequence of the weaker. The last part of the paper introduces uniformly rotund preferences, and s
Constructive notions of equicontinuity
β Scribed by Douglas S. Bridges
- Book ID
- 105842343
- Publisher
- Springer
- Year
- 2009
- Tongue
- English
- Weight
- 199 KB
- Volume
- 48
- Category
- Article
- ISSN
- 0933-5846
No coin nor oath required. For personal study only.
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## Abstract In this paper we provide quantifierβfree, constructive axiomatizations for several fragments of plane Euclidean geometry over Euclidean fields, such that each axiom contains at most 4 variables. The languages in which they are expressed contain only at most ternary operations. In some p
## Abstract This paper continues the investigations begun in [6] and continued in [7] about quantifierβfree axiomatizations of plane Euclidean geometry using ternary operations. We show that plane Euclidean geometry over Archimedean ordered Euclidean fields can be axiomatized using only two ternary